My husband has another woman pregnant. We are now separated. What rights do I have for custody & child support?

You can file for child support right now. No custody will enable you to tell your husband who can and can't be around your child, so you'd better adapt to the fact that there's a new woman and will be a new baby soon. Do everything you can to help your daughter to prepare for that, like telling her that you two are NOT getting back together. You can ask for temporary custody, but again, you can't keep the woman away.