Michigan parents like you are often put into very precarious situations when dealing with child custody issues. It can get personal quickly when you end up in these battles, and the decisions you make can have a lasting impact on whether or not you are viewed favorably by a judge when it comes time to decide who will get the children.
FindLaw takes a look at whether or not it is alright for you to move out of the house and leave your kids with the other parent, and then attempt to gain custody later in battle. Unfortunately, the short answer to that is: likely not. Though there isn't any way of knowing for sure, it's highly likely that you could damage your chances. Leaving the children behind in any capacity can paint a certain picture for the judge that will preside over your trial.
It is possible to take your children with you if you absolutely must move out of the house. Being trapped in an abusive situation is one valid example. This may be interpreted instead as a gesture of protection toward your children. However, you must speak to a court immediately if you do this, as it can be considered unlawfully absconding with children without a court order otherwise.
If this sounds like you, or if you are concerned that this may be you in the near future, consider contacting an attorney as soon as possible. They can help you with your issues and can help guide you down the right path for child custody.