1. Do you want your H to have 50% time with D? What does your lawyer say? I think, in most states, mom's get the advantage. Even though adultery does not affect custody, the fact that he's had an affair and wants to give your daughter 50% to a "step-mom" may have bearing. If you are OK with 50-50 time, then ignore my comment.
2. Remember, if your daughter is 50% with OW and husband, and she's at home, your daughter will see her at least equally, if not more than you.
3. A fair agreement is that regarding custody all decisions about all things regarding your daughter are yours and you husbands. The OW needs to agree to agree with your joint decisions. Haircuts, toys, clothing, sex-ed, television, dating, etc....all these decisions are yours and your husband's. The OW needs to agree.
4. Now to revisit the situation. Why not get full custody and joint custody and your H gets to see D every other weekend and one night a week?
5. Sara is right, your husband wants 2 women, and....he's honestly confused. Being D and living with OW will take it's toll.
6. The OW is a symbol for him of something "other" than you. Perhaps she's more "Suzy homemaker". Maybe she's more assertive. Maybe she wants you daughter AND husband. In may case, my wife wanted the OM to be a father to my children. She was looking for a complete replacement. In fact, it may be the case that he really wanted my kids.
7. Wait until you are divorced to date. You can always tell your daughter you held the moral high ground.
8. Regarding your church. It's your home church. Your husband needs to leave. Even if the elders don't have the courage to discipline him or ask him to stop mentoring the youth, they should, for decency's sake, ask him to worship somewhere elses since you are divorcing and it's the result of his affair. If they don't, then the message they send out is your H has an affair, leaves you, parades his new "family" and mistress in front of the church and you end up leaving. It's stomach churning and obscene. Am I being clear? I have senior contacts in many denominations, including yours, and, if you want, I'd be happy to have someone call your elder board and put the thumbscrews on them. Well, maybe not put "thumbscrews" on them, rather, shed some light. ;-) I'm willing to do it.