1. Hope your both the children and your wife are still residing in your home only?, if that is so, why do you want them separately, I think she has not fled the house yet?
2. You cannot hold her for long if she has decided otherwise, however you can file a criminal complaint against her paramour for adultery.
3. You mean she is giving a false complaint against you, well, let she file it, you can challenge it properly.
4. Let she do it, you can take the help of law.
5. You hold the children and may ask her to give divorce on mutual consent grounds and to leave the house.