He has an empty threat. The standard for family law is the Child's Best Interest, not the social life of the parents. In other words, courts look at what is best for the child. Courts believe that it is in a child's best interest to be with both parents unless one of them is abusive. Your husband sounds psychologically abusive; his behavior will only hurt him later on. Be sure to save any phone records or text messages which shows your husband is trying to control you.
As to living with another man, this should not hurt your chances unless your husband can somehow show that the other man would be abusive or somehow hinder your daughter's development. If this other man is helping you pay your bills and could help you raise your daughter and is not a negative influence on your daughter (ie doesn't do drugs), than this new man might actually help your case (word it carefully though, he should not be a replacement father unless you can prove your husband is indeed abusive).
I am not a lawyer. Please see a family lawyer for legal advice.
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