I really sympathise with your dilemma, we have taken on elderly cats from Cats Protection in the past, in the knowledge that we would have them to the end of their lives and one of whom had very expensive physical ailments. As we are both retired, we could given them the love and care they need, but it sounds as if you are at the end of your tether. I agree with Fleurpepper: contact your local cats' rescue centre for advice and, although it may be hard, accept what they say. It doesn't sound as if either you or the cat can be happy with the current situation, and being cold all day may be making her peeing worse. Could you afford to run a small heater for at least the coldest part of the day?
I wish you all the very best, we had our last cat put to sleep in March after her kidneys failed, and we are still debating whether to get another. Whatever you decide to do, I'm sure you will consider the cat's needs first. 