I'm sorry to say it but some of the advice here isn't legally correct. I wrote and deleted a post as it doesn't sound like OP is in the headspace right now to receive this information so I'm not sure whether it's helpful to overwhelm her. But as OP and her husband are in a long marriage and the house was bought during the marriage, it is now a marital asset and he would be entitled to a share of it if they were to divorce. That is the same whether or not he's on the mortgage and whether or not he's on the deeds, I'm afraid.
This is all a long way off for OP though - most importantly OP should not leave the house if/when he asks her to, she can change the locks but as per the above he would be able to go to court and get an order to re-gain access as the house is also his property. OP's best legal bet is getting a non-mol asap which is very easy to do, can be obtained without service, and then seek comprehensive legal advice before the return hearing. There are lots of very good family solicitors who offer 30-60 mins free advice that OP could make use of and given the sexual abuse OP can also seek legal aid. You can get a non-mol without representation by going to your local family court and asking for the application form. The appointment with a judge is usually 5-15 minutes max and they are very experienced with litigants in person and will be kind/speak in plain language so everything is understandable, there is no reason to fear this if you choose to do so OP, and you can take a friend/family member with you.
ETA - OP if your local family court has a Personal Support Unit I would highly recommend their services for obtaining a non-mol without representation. They cannot give you legal advice or speak in court for you but they will be experienced in completing the form, can tell you what to expect when you go in, and will be able to accompany you in court if you don't have anyone else to go with you. It's free but they are busy so you may have to wait or make an appointment, not sure how they're operating post COVID