I think you need to put your foot down about him coming to your home. As they get older, having him mooching around, being a fun sponge is going to be miserable for the kids and they'll come to dread his visits. Your autistic child, in particular, needs home to be a safe, happy space.
Besides, if they really are the main joy in his life, he will be happy to meet you all at the park, now the weather is getting warmer. If he finds an excuse not to turn up, then becomes "depressed" about not seeing the kids, tough titty for him. At the moment, though, he is being incredibly manipulative. You need to call the shots if he isn't going to be pro-active about making a meet up with the kids about them, rather than him and if he starts on about being drepressed, again, shut the conversation down and ask him when he is planning on speaking to his GP about his depression.
You are not his therapist and nothing you do will make him better, even if you had all the expertise he needed, because it doesn't suit him for that to happen.