Consider going to the doc for your depression and getting on A/D's. Depression doesn't usually go away on its own, you may need medication before it gets better. I went on A/D's for a couple of months and it made a huge difference. After being on them a few weeks the depression lifted and I felt like my old pre-BD self for the first time.
Consider hanging out with the kids somewhere else. Your W doesn't want you there and it's just resulting in a lot of negative interactions. I understand you can't afford to take them out somewhere that costs money but surely there's a local park you can take them to to hang out before their class. Your grand total time in the house should be just long enough to pick them up and drop them off. If you've decided you're not moving back then keep your time there to an absolute minimum.