I'm disappointed in your bike shop. I'm pretty sure my LBS would charge for the tube ($7) but wouldn't charge their usual $10 to install it for someone in your situation. (They don't charge me and my only excuse is that I'm lazy.) It's such a simple job for someone experienced with all of the tools ready at hand. And if you went in twice with flats they would definitely would get to the bottom of the problem.

In my city there is a bike co-op that has a policy of not charging and some locally run shops that I know would be charitable. Cycling enthusiasts tend to be thrilled when a bi/tricycle has enabled someone to be self sufficient in a way that wouldn't be possible otherwise. Perhaps you can find a more sympathetic bike shop.