If you are a stay at home mom and he works he might even get full custody.
I say that because that is what happened to my BFF. Her soon to be ex got full custody and she was ordered to pay spousal support and child support plus half of any child care the ex had to pay for since he worked.
She still, 2 years later is unable to get more than visitation with her kids because she is not financially able to support them without any child support or alimony. This man makes over $100K per year and she did not need to work.
BUT because she didn't have a stable income he got full custody.
So get a job now if you aren't already working. If you are then you are steps ahead of my friend.
Maybe he will be different once he is not living with the kids all the time. Just because he doesn't do a lot with them in his off time does not mean he won't spend a lot of his off time doing all sorts of stuff with them.
I feel bad for your family because they are going to be so disrupted by all this transition. BUT in the long run you'll be a happier mom.
I'd visit with an attorney to find out what the judges have been doing in divorce cases in your area. I see a lot more of the 50/50 custody which I think is so hard on the kids and the parents. One needs the ability to make decisions without the other.
The attorney might be wrong too. My BFF's was. He told her she didn't have to worry about anything. She'd get full custody, child support, and spousal support.
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ETA
I have a friend who is a religious fanatic. I say that in the nicest way, she's real sweetheart but won't even take on cleaning a new person's house without praying and waiting to see what God has to say about her cleaning that person's house. In my opinion he has bigger things to focus on.
She did not want her kids around her soon to be ex's parents because they smoke. The judge sided with her.
So now SHE can't take them to the state fair, the county fair, a carnival, the zoo, no where that outdoor smoking is allowed or seen. If she is at the local vo-tech where smoking on the campus is prohibited and someone lights up she can be taken to court for violating her own court order. If he sees her in any of these places HE can take her back to court.
So if you did try to even say he should limit the kids exposure to anything he can come back on you and you could find you drew a line and can't cross it either.
These poor kids can't perform at Oktoberfest because alcohol is served, they can't go to the fair either. They sell beer there.
So be careful what you try and control with him, it can come back on you too.