There may be nothing wrong with her that would cause her to have a difficult labour again or there may be… you don't know.
First-time lambers can take a long time lambing, you may just have been too impatient (one of my ewes walked around for several days last spring, doing the pawing of the ground looking as if starting and then just getting up again and going for feed - in the end she did her thing and all was fine). I can't see why the vet did a C-section, mine will not do it unless there is a clear indication that something is very wrong and s/he would be unable to deliver any other way and he will not do it if he thinks the lamb (or kid in my case) is dead! Did the vet give you an opinion as to why he thought the problem (if indeed there was one) occurred and he could not go in an get the lambs out but had to do a C-section?
However once done I would not breed from that ewe again and also not sell her for breeding (just because vet call-outs are expensive, and usually more than the ewe is worth, so my risk assessment says - too risky and you will always be able to breed another good ewe!).
I have also found (in goats and in a few sheep) that once they have difficulty in lambing/kidding (serious mal-presentation for example) it does happen again - but I never had to resort to C-section (yet!). But
I don't see why you should assume her offspring is not good, I would try, especially if you a) pure breed and b) can get them scanned to make sure the right amount of feed in the last 6 weeks so not overfat - one of the main reasons 1st timers have difficulty in lambing/kidding.