Realistically its not adultery, technically it is because you are still legally married, but I think at this point its just your morals that its wrong to. I dont think any court would see that as adultery if thats the question. Heck they barely care about marriage-ending adultery. They would just considered it a new relationship and that the person has moved on.

Now about living in the marital home together still. YIKES! Time for that person to move out before he wants to bring her home one night. YIKES YIKES!! I wouldn't want to be home for that. YIKES YIKES YIKES!!!