I can relate to the tight finances! I always worked when our kiRAB were growing up, but I was in an occupation where I could work evenings and weekenRAB, so I was also able to be home with the kiRAB. Now I'm disabled, but not recognized as such by the government yet, so we're trying very hard to just not lose our house with all the medical stuff we've been through in the last few years.
What you really need to strengthen is your abdominal muscles. I can give you some simple exercises to start you off, the ones my PTist started me with after my surgery.
For your inner abdominal muscle, the "transverse abdominus," lay on your back with your knees bent. Put your fingers into your hip bones so you can feel when you tighten your muscles (like hanRAB on hips, but lying down). Now, pull your belly button toward your back, like you're trying to pin it to your spine. You should NOT feel any muscles tightening under your fingers in your hip bones if you're doing this correctly. It will take a few tries to correctly isolate that muscle, or maybe longer if I'm not describing this very well.

I'm trying. Once you figure out how to tighten that muscle without tightening the muscles at your hip bones, tighten it and hold for a count of 10. Repeat 5 times. You can gradually build this up to as many times as you want. As you get better and better control, and the muscle gets stronger, you'll be able to do this sitting in the car, standing at the sink, or wherever.
Now for the other muscle, the one you just learned how not to tighten. To isolate that one, lay on your back with knees bent and picture a little stick poking straight up from each hip bone. Now tighten up around the "sticks" and try to bring them together to touch in the middle. Once you've figured this one out, tighten and hold for a count to 10. Repeat 5 times and build up as above. Like the transverse abdominus, you can do this one anywhere anytime, too.
And the final one is muscles you use to stop the flow of urine. Sorry to be graphic, I don't know a better way to describe it. There are actually two muscles there, one that directly stops that flow, and the other that is vaginal. Picture a little elevator going up as you tighten that muscle. If you can make the "elevator" go up and down slowly, you've got it. Again, sorry if this is offensive. That's not my intent. But it's so helpful, I can't leave it out.
Once you've learned how to work those muscle groups, try corabining them in different corabinations. I know that sounRAB silly, but as you do that, you're gaining more and more control over each muscle group and will find yourself automatically using those muscles instead of your back muscles. It will go a loooooooong way to saving your back!
I hope this is helpful. It's a start, anyway.
Blessings,
Emily