The next thing to do is book another solicitor's appointment. Now that you know the truth you need to start the papers going. You need especially to make financial arrangements. I'm sorry, I've forgotten if you are a SAHM or if you work outside the home, but this is especially important if you have no, or very low, income. You need to see what you can do, if anything, about getting him to leave.
He sees himself and you 'living apart in the same house' with no need to change things. It works very well for him, doesn't it, because he sees you as continuing to take care of DD and do all the domestic chores. In other words, you've been 'demoted' to maid of all work and nanny whilst he gets to live the 'single life'.
Starting tomorrow, make it very clear to him that you will NO LONGER provide any 'domestic services' for him. You will no longer do his laundry, cook for him, run errands for him, clean up after him, or run his 'social calendar' (his family gifts, cards, etc). That you will continue to look after DD and yourself but that's it!