They reset the phones, did not put in new SIM cards and sent us on our way. When we got home, tried to use the phones, the same problem happened.
Why did you not check the phones before you left?
Everything I've ever had worked on, I made sure worked before I left. This ranged from computers to sewing machines.
Based on the above response, it sounds like you don't have coverage.
T-Mobile's coverage maps are estimates -- They're based on some magical formula muggles like me don't really understand, but the consensus is it's generally over-estimated when people are complaining (I don't know of a location it's under-estimated -- I'm sure they exist, but nobody complains about those). The coverage can range based on unknown barriers between device and tower (this is generally building structure concerning indoor coverage), but this is truly the reason carriers give a 14-day window to try the coverage in places you need it before you are forced to commit.
What doesn't make sense is if the devices worked for 10 days at home (that's what I'm now interpreting in your post) and just magically stopped. The only thing I can think is you had WiFi Calling on for those 10 days and then turned it off. But, that's purely conjecture.
I guess the important thing is you managed to determine T-Mobile's network doesn't work for you where you live at this time.