Good luck to the second wife, and to the third, and so on. The main topic to explore at this stage is the eligibility of the man to take on a second, third, and fourth wife. Yes, Islam did allow the man to marry up to four wives, and that's something men never ignore. To remind all of us of these restrictions. The second and most important restriction is fairness.
Humans can never be fair, no matter how hard they try.
However, going back to the original subject, I think it is up to the wife to decide to stay or to leave, with or without her kids. The children are the victims in such situations. Divorce is not the solution, however. The first wife doesn't have to put up with the husband any more. This is a torture, no woman should go through this any more.