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You have a right to bring this up during the divorce proceedings, to voice your concern about where your daughter will be sleeping and what the conditions are. You should tell the judge (or the mediator, if you two participate in mediation) that you do not have any problem with your daughter spending time with her father but you want to be sure that they (either your husband or his family members) will not be having non-family members spend the night when your daughter is there.
It is important that you tell the judge that you are not trying to prohibit your husband from spending time with his daughter, just that you are concerned about what your daughter sees going on, because your husband might try to turn it around and make it seem like you are just being vindictive.
The judge cannot order anything against other people (he can't order the brothers not to bring girlfriends to spend the night when your daughter is there) but you could ask that he not be allowed to have overnight visits under those conditions. Especially if your daughter is having to share a room or sleep on a couch as opposed to having her own living space.
As for taking your daughter out of the country, he should not be allowed to do this without your consent. You should only consent if he gives something as assurance that he will bring her back. Many courts order the parent to post a bond that is enough to cover your legal expenses if he fails to bring her back and you have to hire an attorney to get your daughter back. I would ask for at least a $20,000 bond.
Christina - if he is being uncooperative, despite the fact that you have given him all the time he asks for, then you have to take control of the situation. Tell your attorney to ask the court to order mediation, otherwise nothing will get resolved.
Things can go badly very fast when one parent allows the other to deviate from the regular visitation schedule. Therefore, I always tell my clients that it is best to stick to what the court orders, at least in the beginning. If you don't have a court order yet, you should ask the court for a temporary order of child support and visitation based on your state's minimum guidelines. I know it may be difficult because you want to be cooperative and makes things go smoothly, but as you have seen, usually the cooperative parent gets taken advantage of. Get something ordered by the court as soon as possible so that you both know what your rights and responsibilities are.