Question: Who is the mother-in-law of Quintus Caecilius Metellus Celer?

Lesbia
Lesbia was the literary pseudonym used by the Roman poet Gaius Valerius Catullus( 82–52 BC) to refer to his lover.
Lesbia is traditionally identified with Clodia, the wife of Quintus Caecilius Metellus Celer and sister of Publius Clodius Pulcher; her conduct and motives are maligned in Cicero's extant speech" Pro Caelio," delivered in 56 BC.
Lucius Caecilius Metellus Calvus
Lucius Caecilius Metellus Calvus( c. 200 BC or before 178 BC – after 136 BC) was a Roman statesman.
He was a son of Quintus Caecilius Metellus and brother of Quintus Caecilius Metellus Macedonicus.
First Calvus used to be a Praetor, later a Consul and Governor of Hispania in 142 BC, where he fought, without success, against Viriathus, then he became a Proconsul of Cisalpine Gaul in 141 BC, and in 140 BC — 139 BC he was a Legate.
In 140 BC — 139 BC Calvus participated in an Embassy to some Eastern states.
Quintus Caecilius Metellus (consul 206 BC)
Quintus Caecilius Metellus( c. 250 BC – 175 BC) was a son of Lucius Caecilius Metellus.
He was Pontiff in 216 BC, Aedile of the Plebeians in 209 BC and 208 BC, Consul in 206 BC, Dictator in 205 BC and Ambassador at the Court of Philip V of Macedon in 185 BC.
He served as a Legate in the army of Gaius Claudius Nero and fought in the war against Hannibal.
In 201 BC he was part of the commission appointed for the repartition of the terrains of Samnium and Apulia for the soldiers who fought in the war.
He was also distinguished as an orator, being counted among his best speeches the funeral sermon pronounced at his father's funeral.
He was the father of Quintus Caecilius Metellus Macedonicus and Lucius Caecilius Metellus Calvus.
Gaius Servilius Vatia
Gaius Servilius Vatia was a Praetor in 114 BC.
He married Caecilia Metella, born c. 170 BC, daughter of Quintus Caecilius Metellus Macedonicus.
By her he had:
Marcus Caecilius Metellus (consul 115 BC)
Marcus Caecilius Metellus was one of the four sons of Quintus Caecilius Metellus Macedonicus.
He was Moneyer in 127 BC, Praetor in 118 BC, Consul in 115 BC and from 114 BC to 111 BC Proconsul of Corsica and Sardinia.
He was sent to Sardinia to suppress an insurrection on the island, which he succeeded in doing and obtained a Triumph in consequence in Quintilis( July) 113 BC.
The same day, his brother Gaius Caecilius Metellus Caprarius also received a triumph for his victories in Thrace.
Caecilia Metella (daughter of Metellus Celer)
Caecilia Metella was daughter of Quintus Caecilius Metellus Celer and Clodia Pulchra.
She was an infamous woman in Rome during the late Republic and a celebrity of sorts.
Quintus Caecilius Metellus Nepos (consul 98 BC)
Quintus Caecilius Metellus Nepos( c. 135 BC – 55 BC) was a son of Quintus Caecilius Metellus Balearicus.
He was a Consul in 98 BC, having fought at the Iberian Peninsula against the Celtiberians and the Vaccaei, suffering before these a memorable defeat.
He married Licinia Prima, after she had divorced Pontifex Maximus Quintus Mucius Scaevola, of whom she had Mucia Tertia.
They had two children:
Quintus Caecilius Metellus (tribune)
Quintus Caecilius Metellus( 11031 BC) was a son of Quintus Caecilius Metellus Creticus.
He was a Tribune of the Plebs and later one of Mark Antony's Generals at the Battle of Actium.
By adoption he had:
Quintus Caecilius Metellus Celer
Quintus Caecilius Metellus Celer (before 103 BC or c. 100 BC – 59 BC) was a consul in 60 BC and son of Quintus Caecilius Metellus Nepos, or, according to some, the son of Tribune Quintus Caecilius Metellus Celer while the latter is the son of Quintus Caecilius Metellus Nepos.
Previously he held the offices of Praetor and Augur in 63 BC.
During the Third Mithridatic War (73-63 BC) against Mithridates VI of Pontus and Tigranes the Great of Armenia, Metellus Celer was a lieutenant (legate) of Pompey during his eastern campaigns (66-63 BC).
In the winter of 66 BC Oroeses, king of the Caucasian Albanians attacked the forces of Pompey while they were celebrating the festival of the Saturnalia in their winter quarters in Lesser Armenia.
Pompey had split his army into three divisions.
Metellus Celer was in charge of one of them and custodian of Tigranes the Younger of Armenia.
Metellus vigorously repulsed Oroeses while Flaccus and Pompey, who were in charge of the other two divisions, defeated the other Albanians.
In 63 BC, when the Catilinarian Conspiracy was discovered Catiline, its leader, was indicted for violence.
He went to stay at the house of Metellus Celer to allay suspicions as Metellus was the praetor, but was unsuccessful.
Metellus then brought several conspirators to trial by virtue of a decree of the senate and imprisoned them.
Cicero entrusted matters outside Rome to Metellus Celer.
He was sent to the district of Pisa (in Etruria) with three legions.
On learning that the rebels were advancing towards Pistoia to flee to Cisalpine Gaul (in northern Italy) he encamped at the foot of the mountain from which they had to descend for their passage to Cisalpine Gaul, while the consul Antonius had his troops at their rear.
He besieged Faesulae (Fiesole), the base of Catiline, together with Antonius.
The two men were encamped in two different places.
Catiline attacked Antonius instead of Metellus, even through the former had a larger army.
References to Metellus Celer during the conspiracy were also made by Cicero and Valerius Maximus.
When he was consul in 60 BC Metellus Celer sided with the Optimates and vigorously opposed Pompey in everything because he had divorced his sister.
Together with Cato
the Younger he was the main opponent of the ratification of the acts Pompey had made with the cities and kingdoms in Asia as a result of the Mithridatic War.
He also opposed an agrarian bill proposed by Flavius, a plebeian tribune, which Pompey sponsored and which was intended to give land grants to Pompey's discharged soldiers which they were entitled to.
Metellus led the opposition to the agrarian bill.
He contested every point of Flavius' bill and attacked him so persistently that the plebeian tribune had him put in prison.
Metellus wanted to convene the senate there and Flavius sat at the entrance of the cell to prevent this.
Metellus had the wall cut through to let them in.
When Pompey heard this he was afraid of the reaction of the people and told Flavius to desist.
Metellus did not consent when the other plebeian tribunes wanted to set him free.
In 59 BC Metellus Celer and Cato the Younger for a time refused to swear obedience to the agrarian law of Julius Caesar, who was consul in that year.
Eventually they complied.
During Metellus Celer’s praetorship, Titus Labienus indicted an old backbench Optimate senator, Gaius Rabirius, for the murder of Lucius Appuleius Saturninus thirty-six years earlier.
Saturninus had been opposed by the consuls of the time at the direction of the senate.
Thus, with the proposed trial the senate would lose the authority to enforce its decrees.
Acts which had received the approval of the senate and had been committed many years earlier tended to give immunity to those who tried to repeat the conduct of Saturninus and make punishment of such acts ineffective.
The senate was outraged that an innocent elderly man of senatorial rank was attacked and that the tribunes were entrusted with the control of affairs.
There were pro- and anti-prosecution factions.
The former won through the support of Julius Caesar, who was the judge together with Lucius Julius Caesar, and Rabirius was charged.
The judges had been unlawfully chosen by the urban praetor, Lentulus Sura, instead of the people.
Rabirius appealed and would have been convicted by the people, but this was prevented by Metellus by obstructing the meeting of the assembly of the people.
Metellus Celer was married to his cousin Clodia Quadrantaria, often referred to in scholarship as Clodia Metelli ("Clodia the wife of Metellus"), the daughter of Appius Claudius Pulcher.
They had a daughter named Caecilia Metella, like all the women in the family of the Caecilii Metelli.
Quintus Caecilius Metellus Celer died suddenly in 59 BC--according to some poisoned by his wife, who was notoriously debauched, reputed to be the incestuous lover of her brother Clodius, of Caelius, possibly of the great lyric poet Catullus (most authorities identify her as the subject of his "Lesbia"), and many others.
Clodia Pulchra (wife of Metellus)
Clodia (born Claudia, c. 95 or 94 BC), nicknamed Quadrantaria, and occasionally referred to in scholarship as Clodia Metelli ("Clodia the wife of Metellus"), was one of three known daughters of the ancient Roman patrician Appius Claudius Pulcher and either Caecilia Metella Balearica, or her cousin, Caecilia Metella daughter of Lucius Caecilius Metellus Diadematus.
Like many other women of the Roman elite, Clodia was very well educated in Greek and Philosophy, with a special talent for writing poetry.
Her life, immortalized in the writings of Marcus Tullius Cicero and also, it is generally believed, in the poems of Gaius Valerius Catullus, was characterized by perpetual scandal.

Answer: Caecilia Metella Balearica