He could be the father...it she's 6 weeks along, it's possible he was still carrying some fertile sperm after his neuter, for several weeks.
Amy, do not beat yourself up over any of this. It has been one big unfortunate accident, and you've certainly done the best you could...add into the mix that she ran away for several days, and that only further complicates everything.
If it were me (and normally I wouldn't say this), I would allow her to have the kittens...it's almost too late to really do anything else. There are a few organizations and rescues that will spay a queen in any phase of pregnancy, but that's a tough decision to make. If you choose to allow her to deliver, check into the possibility of finding a foster mommy through a rescue organization that can keep Nina and the kittens through the birth and up through the weaning process. After the delivery, have Nina spayed immediately...this may mean the kittens may have to be bottle fed temporarily, and that's okay. Once the babies have found homes, Nina can return home to you. I know that sounds like an awful lot of shuffling around for Nina, but it would take a load off your plate, and having Nina spayed either now (thus aborting the kittens), or immediately after the kittens are born, will be such a big relief to you.
It's up to you! Whatever you decide, we all understand. It's a tough position you're in, and we know whatever you do, you'll do it with Nina's best interest at heart.