Sorry this is long....
Hi SJ! Good to see you around, even but sorry to hear about all you're going through.:-( But, it's reassuring to hear you're anxious to get back to working out! As for working the chest and back, it might be hard with the weights you have since they're not that heavy for chest/back, especially for someone who's worked out awhile, like you have.
For chest, push ups are a great exercise, even on the knees, if you can't go up on your toes. If you could get a tube, you can put it behind your back, hold the handles in your hands (or tighter) and that'll add resistance. You can do chest press and flyes on the floor (or an ottoman) but I'm guessing the weights won't be challenging enough. You could do superslows with the weights you have:
For the back, you could do lat pull overs:
You can do it on the floor, just rotate the dumb bells so they're parallel to the floor. Another possibility is to do a back row from a plank position (on your knees, if you can't do it on the toes) with your hands each on a dumb bell and do a row from this position. It'll also hit your core. I think a tube would be a cheap addition to what you have and would give you a lot more options, eg. back rows with them around your feet. Or, tied to something sturdy opens a host of options. Let us know if you can get one, and I'll give you more suggestions. Hope that gives you a start! Let us know how it goes.
I will try pushups from the knees - I can't put weight on my toes and have been doing modified pushups in Pilates since the break - and no pushups at all
Bleah, sorry, I meant one arm rows, not both arms!
I tried the push ups last night, and I did the 'cross the foot' thing - worked pretty well.