Henry Brigden Park is on Thurston Street and Blaxland Avenue in Penrith, and they have recently added a sun shade to it. This is another park that is basic, but there is definitely enough for the kids to do. During lock downs I gave up coming here as there were often other families there too, but now it seems to be fine. It is surrounded by apartment blocks, and I think I just went a few times when there were already two and three other families there and there just isn’t enough in this park for that many families.
There is a big slide, my kids were initially scared to go up to it but that might be good for your situation, a pretend cafe, a flying fox, and swings. There is a seat from parents, it isn’t close to the park but the park is set on a large block and it is not close to the road. Even so, I don’t sit on the seat I end up standing or sitting on the larger swing.