If cost isn't a problem, you can ask the vet to do pre-surgery bloodwork. It's not usually necessary for young, healthy dogs, but it will help set your mind at ease to know if their internal organs are working properly (which is important for metabolizing the anesthetic safely). If you can, talking to other people who have had their pets neutered by that vet will ease some of your worries.
Neuters are very simple surgeries, with few complications. The anesthetic is the biggest worry, which is why you might want to go for the bloodwork. The retained testicle will cause the vet some extra work, but it's not a big deal. The surgery for that doggie will probably cost extra.
As for staying with them the entire time, this is probably not possible. Even if it were possible, it's not a good idea. Even some vets and vet techs don't like to do surgeries on their own pets, since it's so weird seeing them under the anesthetic. Very eerie, trust me---I once took a feral cat home from her spay while she was still fully under, and it was unsettling. And, you don't want your boys associating you with the vet's office. It's much better to just drop them off, let it all happen the way the vet has been trained to do it, and pick them up when they're feeling better.
You can ask for pain pills for your babies. A lot of vets don't offer them for routine neuters, but if you want to give them a little extra comfort, they are an option. The vet may have a good reason for not wanting to give them pain pills, but you can at least ask.
If you have any doubts about your vet's skills, or think you're just being brushed off, try another vet. You want to find a clinic where the vet and the vet techs/assistants all care for your boys very much. If they fuss over them while they're in for routine stuff, that's a good sign
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