They are notoriously lazy! If could be months until he actually files and remember you dont have to sign anything! Im assuming you have assets and then thee is child maintenance and childcare split. They all think Its going to be so so easy and done, but it never is!
I dont know where you are and what laws would apply, but can you get some legal advice to know what a split might look like?!
I would say him moving back in is a hard no Rachel. I do think you need some support, a friend, family, councillor, its though being on your own with three kids.