I don't feel as if I'm the best person to give you advice on this subject.
But I will share my feelings for whatever they are worth. Please don't hold these thoughts as the answer, as they are simply my own opinion.
Everything you do towards your H can be percieved by him as an attempt to control him or manipulate the situation. As you know, this will bring about more anger and resentment towards you.
As a father he has rights to see his D. As long as everything he does with her is not illegal or abusive, IMO is out of your control to make it the way you think it should be.
As much as you feel your D will be affected by your H having your D spend the night at OW, she will be equally affected by your fight to prevent it. My suggestion is to "let go."
The more energy you give to something you do not want to happen, the greater chance that it will happen. By giving energy to something you give it life and feed it.
How you handle the MLC situation with your H, will have the biggest impact on your D and how she learns about values and appropriate behaviors.
You can set the standard for, honesty, trust, love, compassion, integrity, respect for life, commitment, pride, confidence, loyalty, individuality, caring, family and faith.
The "core values" that you live by will be the best gift you can give to your D. Let go of your H being the teacher of "values" for your D. He is not in a frame of mind to be the teacher, so it needs to be your role at this time.
I realize you want to protect your D. But how will she learn the values that you hold dear to your heart if she does not also experience the opposite?
We learn from our experiences. Experiencing bad things is not all bad. If it were not for the painful experiences I had during childhood, how could I have become the person I am today?
My advice is to let go and turn it over to God.
The best gift a LBS can give to their children is how well they treat their MLC spouse. Our children are watching and observing and will take what they have learned into their adult relationships.
If you had a choice, what type of relationship with their spouse would you desire for your children when they get married?