More information would help, J.. Is he potty trained? Does he only do this at night? Does he wake up to pee during the night, or does he just do this when he's supposed to be going to sleep? Does he need more adult help getting to the bathroom? Would a potty chair in his room be a possible solution?
Shared custody can be difficult and confusing for children of any age, and probably much harder for toddlers. Depending on how he feels about your bf and how much of your attention you give your bf while your son is with you, he could be pleading for more attention, or experiencing a regression in potty training because he's unhappy with his family life. Your bf could actually be contributing to the problem, too, if he is either competing with your son for your time or coming down hard on him for behaving like a 3yo child. I hope you are putting your little guy's needs as your highest priority. He can't help the life that's been handed to him.
There's a lovely little book you might want to read, How to Talk So Kids Will Listen, and Listen So Kids Will Talk, by Faber and Mazlish. I started using these techniques with my grandson when he was around 3, and have been very impressed with how well the techniques not only help the child get to the root of his problem, but also that the child participates in coming up with solutions. Kids love the validation and respect, and work hard to make their remedies work.