Have you considered trying to learn meditation or some other non excersize relaxation technique ? I could never sleep well either (turned out I had sleep apnea so no wonder!) But I felt much better when I meditated even though I was getting poor quality sleep. Alone I think the meditation is helpful but in your case it might also help you wind down to sleep sooner.
It really looks like you are doing everything you can in spite of everything you have going on. You should be very proud. I'm having a hard time just taking care of me you are responsible for the happiness of three other people and it looks like you are doing really really well!
*hugs*






Patience and perseverance pays off.