In theory, there should be no such thing as an affair or illegitimate children. Men are compelled to take full responsibility for the children they bring into the world. To that end, fathers, technically, always retain full custodial rights. Those drawn to polygamy because they wish to exploit women will have a rough time with Islamic rules governing multiple marriages. Many times this is relative to what the parties agree on.
Different women have different goals.
Some households may be combined, but wives are under no obligation to live together. They also are under no obligation to work outside the home. Even if they do, the money they make is their own. The practice is more prevalent in other parts of the world where it may be seen as more practical or where pre-Islamic cultures were already entrenched in multiple marriages. Even so, polygamous marriages account for less than 5 percent of all Muslim unions.