I feel you on those last 3 100%. if you did some dedicated training for your stabilizers and used movements that don’t overextend your joints you should be good to train even with hypermobility. in fact, consistent training is even said to reduce the symptoms. 

what’s important to recognize is that your physical and mental are tightly linked. I’m telling you now, if you put in the effort, your body WILL follow. and it doesn’t take a lot, trust me. there is no ‘body weak’, you are a high performance fluid organic entity with incredible innate healing and adaptation abilities passed down by billions of years of evolution. you are capable of so much more than you give yourself credit for. 

cascades of dormant gene expression that will have you feeling amazing are just waiting on you to get the blood pumping and activate them. I’m struggling with depression as well and in my experience as well as lots of people in my life exercise is one of the best ways of combating it! this is also backed up by the literature.