Thank you for using Just Answer for your needs. Here are some guidelines that TireRack recommends...
I can tell you that by your description, even at our Dealer, we also would not repair and install your tire. Because if we did, we would be taking on the responsibility for anything that may happen in the future. You do remember the Ford/Firestone Tire rollovers fiasco don't you? That whole incident is the reason that as of 2008 every new car or truck sold in America has a tire pressure sensor installed. There were quite a bit of lawsuits and even deaths that occurred because of that.
This also boils down to whether your tire dealer wants to take on the responsibility of a possible accident just for installing 2 used damaged tires. I know I wouldn't. Here is one of the last lines from the article above....
Driving on an improperly repaired tire is dangerous because it can further damage the tire and/or allow its strength to deteriorate over time. An improperly repaired tire driven at high speeds may suddenly fail, causing loss of vehicle control.
This above statement would also include a tire that should not have been repaired in the first place. I would recommend that you take the tires back to the original owner and have them replaced with another set, at least the one tire that is bad. You and your family's life is too important.