OP You could be me! I have had a long lasting depression (mixed with bereavement) since my children were born and the oldest is 5. It's only been the last 6 months or so that I have started to feel better.
As well as finding play hard I've had trouble with my temper. I feel so guilty about it all, as though I have ruined my children's lives as they've had this terrible start to life with me.
I remember every day feeling as though getting to the end of the day was like climbing an enormous mounting!
I don't have much patience which doesn't help with the play thing as they make up weird rules as they go that just makes me not want to do it anymore. There are some things with I find easier though and I tend to just try to do those, although I have to make myself do it quite often. At the moment I'm just trying to make myself spend a chunk of time with each of them each day. It's not even that much, maybe 15 minutes so I feel terrible that I have to make myself do it. I am hoping though that if I keep doing it, it will become a habit.
The things I find easier are reading, drawing, hunting for bugs in the garden, going for walks and exploring, simple craft projects, cuddling, puzzles etc
The only way that I managed when they were younger was to go to play groups/baby groups, meet other mums and make friends. Then we used to meet up with them a lot and the children would play and we could have adult conversation and I would get some peace (oldest is demanding). I felt terrible about that as it was totally for selfish reasons but I knew they would benefit from it too. Sometimes you just have to do what you can to get through the day.