The Godfather Part II

In 1901, the family of nine-year-old Vito Andolini is killed in Corleone, Sicily, after his father insults local Mafia chieftain Don Ciccio. Vito escapes to New York City and is registered as "Vito Corleone" on Ellis Island.
In 1958, during his son's First Communion party at Lake Tahoe, Michael Corleone has a series of meetings in his role as the Don of his crime family. Corleone caporegime Frank Pentangeli is dismayed that Michael will not help him defend his Brooklyn territory against the Rosato brothers, who work for Michael's business partner Hyman Roth. That night, Michael leaves Nevada after surviving an assassination attempt at his home.

In 1917, Vito Corleone lives in New York with his wife Carmela and son Sonny. He loses his job due to the nepotism of local extortionist Don Fanucci; he is subsequently invited to a burglary by his neighbor Peter Clemenza.
Michael suspects Roth of planning the assassination, but meets with him in Miami and feigns ignorance. In New York, Pentangeli attempts to maintain Michael's faÃ§ade by making peace with the Rosatos, but they attempt to kill him.
Roth, Michael, and several of their partners travel to Havana to discuss their future Cuban business prospects under the cooperative government of Fulgencio Batista; Michael becomes reluctant after reconsidering the viability of the ongoing Cuban Revolution. On New Year's Eve, he tries to have Roth and Roth's right-hand man Johnny Ola killed, but Roth survives when Michael's bodyguard is discovered and shot by police. Michael accuses his brother Fredo of betrayal after Fredo inadvertently reveals that he'd met with Ola previously. Batista abruptly abdicates due to rebel advances; during the ensuing chaos, Michael, Fredo, and Roth separately escape to the United States. Back home, Michael learns that his wife Kay has miscarried.

Three years later, Vito and Carmela have had two more sons, Fredo and Michael. Vito's criminal conduct attracts the attention of Fanucci, who extorts him. His partners, Clemenza and Salvatore Tessio, wish to avoid trouble by paying in full, but Vito insists that he can convince Fanucci to accept a smaller payment by making him "an offer he won't refuse". During a neighborhood festa, he stalks Fanucci to his apartment and shoots him dead.
In Washington, D.C., a Senate committee on organized crime is investigating the Corleone family. Having survived the earlier attempt on his life, Pentangeli agrees to testify against Michael, who he believes had double-crossed him, and is placed under witness protection.

Now a respected figure in his community, Vito is approached for help by a widow who is being evicted. After an unsuccessful negotiation with Vito, the widow's landlord asks around, learns of Vito's reputation, and hastily agrees to let the widow stay on terms very favorable to her. In the meantime, Vito and his partners are becoming more and more successful, with the establishment of their business, "Genco Pura Olive Oil".
Fredo is returned to Nevada, where he privately explains himself to Michael: resentful at being passed over to head the family, he helped Roth in expectation of something in returnâunaware, he claims, of the plot on Michael's life. Michael responds by disowning Fredo.
Unable to get to the heavily-guarded Pentangeli, Michael instead brings Pentangeli's Sicilian brother to the hearing. On seeing his brother, Pentangeli denies his previous statements, and the hearing dissolves in an uproar. Afterwards, Kay reveals to Michael that her miscarriage was actually an abortion, and that she intends to take their children away from Michael's criminal life. Outraged, Michael takes custody of the children and banishes Kay from the family.

Vito visits Sicily for the first time since emigrating. He and business partner Tommasino are admitted to Don Ciccio's compound, ostensibly to ask for Ciccio's blessing on their olive oil business. Vito exacts his childhood vengeance by knifing Ciccio after revealing his old identity, but Tommasino is shot in the leg and suffers a permanent disability during their escape.
Carmela Corleone dies. At the funeral, Michael appears to forgive Fredo but later orders caporegime Al Neri to assassinate him out on the lake.
Roth is refused asylum and even entry to Israel and is forced to return to the United States. Over the dissent of consigliere Tom Hagen, Michael sends caporegime Rocco Lampone to intercept and shoot Roth on arrival. Rocco, however, is shot dead by federal agents after completing his mission.
At the witness protection compound, Hagen reminds Pentangeli that failed plotters against the Roman Emperor often committed suicide and assures him that his family will be cared for. Pentangeli later slits his wrists in his bathtub.

On December 7, 1941, the Corleone family gathers in their dining room to surprise Vito for his birthday. Michael announces that, in response to the attack on Pearl Harbor, he has left college and enlisted in the United States Marine Corps, leaving Sonny furious, Hagen incredulous, and Fredo the only brother supportive. When Vito arrives, everyone leaves the room to greet him, leaving Michael alone at the table.
Michael sits alone by the lake at the family compound.

Question: why Kay intends to take their children away from Michael's ?
Answer: Michael's criminal life; Michael's criminal life