Just to give the other side of the coin.
My wife and I have recently agreed that our relationship, such that it was, had died and that we both would benefit from going our seperate ways.
We have put our house on the market, splitting the equity when it sells 50/50. I may have brought more money into the home over the years, but she had the girls, ran the home, sorted the accounts etc so evens out.
Neither of us can afford to rent while still paying the mortgage. Ww do everything seperately. Seperate rooms, don't eat together, don't go out together. The only thing we do share in common is our 4 year old grandson.
I can produce numerous people who will confirm our situation, it isn't a secret.
It may be he has agreed to look after his kid(s) on certain days/times.
I work mainly from home so I am around a lot to collect him from nursery, give him lunch etc. This would involve me being back by a certain time on those days, which may be the case here.
But if I am ever lucky enough to meet a woman who cares I would openly explain the situation.