Something very like this happened to me (name changed).
My experience was very negative. My ex gave up trying to look for work - before eldest child was born he’d been doing so. He wouldn’t do any activities with our children, playgroups etc. I felt this disadvantaged them socially. The house was always a tip. I’d get home late & have to put kids to bed, clean do laundry etc. He didn’t even bath them.
He started using drugs quite heavily & became violent & threatening to me - on one occasion knelt on my buttocks smashing my face into floor. On another raped me. Took the kids with him to buy drugs. Drove them about while high. Frightened kids while shouting at them - couldn’t control his anger.
I was advised by my solicitor (actually, by two solicitors!) that if I left him he would - despite all the drugs violence & anger! - get full custody & the house. I’d end up paying the huge mortgage, living in a bedsit & seeing kids every other weekend. Because he was the ‘primary carer’ - absolute bullshit.
When I reported the violence to the police they told social services. Because I couldn’t leave him, I had to stop reporting the violence - I was afraid social services would require us to live separately & I’d have to leave the kids with him.
I spent years in a miserable relationship because I couldn’t leave him- when I’d never even wanted him to stay at home! I wanted him to get a job!
I was astonishingly lucky: his financial position changed (large & unexpected inheritance). I was able to do a deal with him- I wouldn’t make a claim against his money (he suddenly had lots, and wanted to keep it!) if I got primary custody of the children. Basically if it wasn’t for that I’d still be trapped.
This was some years ago & writing this makes me realise how awful it was. I would now advise anyone - male or female - to be very very very wary of having a full time stay at home partner. It can work, sure. But it can be a hideous trap. It was for me. Only do it if you’ve got a strong relationship, have talked it through, and crucially if it’s genuinely what you both want. It needs to be a conscious mutual decision, not something driven by one partner or that you just drift into.