I'm going to be the spanner in the works here and say that I was in the similar position of dating a man who was separated but living with his wife, and a lot of what you describe was similar, but he has now moved out, bought his own place and we are together.
He had stayed at home because of his children for a number of years, but once they separated he stayed for another three years whilst his son went through exams and to support his daughter with some ongoing MH issues (still has, but she has been able to hold down a p/t job for a little while now). His children were fully aware of the separation.
I was under the radar throughout this time (about 18mths of the 3yrs they they were separated) because he didn't want to rock the boat, introduce someone to his children who might not stick around, and generally because his wife didn't want the separation and became quite difficult, and continues now to be quite nasty. They weren't having sex in that time or for a long time before (and I've seen messages from her to that effect).
In our early days he told her when he was going on a date as they'd agreed but despite saying she was ok with it, she really wasn't and took her upset (which she's entitled to) out on the whole family, so it suited us better to keep it quiet. We've had plenty of weekends away, etc but I would never have wanted to go to his house and meet her!
It was tough when he went back to the family, especially when I knew he didn't want to either, but I never ever felt like he was putting her first. His kids, yes, but not her.
There were no financial reasons why they couldn't split (significant assets she is getting half off) but he has readily admited that the thought of moving out when they first separated and not seeing his kids eery day and being lonely really wasn't very appealing, so they made the best of it. He'd love me to move in with him now but we both want to enjoy a bit more public dating and getting to know each other's family and friends before we do.
I'm not saying this is your situation at all, but in my experience, there are some genuine cases out there! Should he have waited until he'd moved out before dating? Maybe, but it's worked out for us.