I haven't heard of a vet suggest pain medication is
bad for rabbits after surgery--females especially need it, since it's quite a big operation.
Keep in mind, though, that receptionists most often deal with cats and dogs, so their advice doesn't always apply to rabbits. Did you have any recommendations from the actual
vet specifically (not the receptionist)?
And did they give you any pain medication (like meloxicam) to take home at all? Or any gut stimulant (can't remember the medical name for it--it's to keep rabbits' guts working until they start eating again properly)? Those two are almost always prescribed after surgery for use at least during the first 1-3 days afterwards. Not sure about the gut stimulant, but you should be able to pick up meloxicam (pain relief) from most vet stores.
I would not separate the rabbits
unless they are fighting or harassing each other. If you absolutely must separate them, then make sure they can still see/hear/smell/touch each other, e.g., through the bars of a cage, even if they can't have full contact.
From my understanding and experience getting my girl fixed, a little dried blood around the wound isn't necessarily cause for concern. My girl's stitches were subcutaneous, but I imagine dried blood on the stitches is similarly not cause for alarm if all else looks well
(but maybe someone else will correct me). But if the wound is actively bleeding, swollen, or remains red, then you should contact the vet.
The first time my female bunny underwent surgery, the vet neglected to prescribe pain killers, and she took a very long time to recover. After about day 3 when she was still struggling, I insisted they prescribe pain medication, which definitely helped her. But because we had waited so long to give her pain relief (this is what the vet said), the pain had set in so intensely that we had to keep her on pain medication for about a week to ten days. I learnt the hard way--rabbits after an intense surgery (especially females) should always
have pain medication on hand!
Apart from all that, she might not start eating and pooping fully normally again until a couple days, but she should start pooping and eating
something (even just a nibble on some greens) within the first 12-24 hours. If she's still not eating (or pooping)
anything at all after 24 hours, you should call the vet. In my experience, they usually like to start eating greens first (grass, celery leaves, nice soft things like that), then hay and pellets come much later. Try to entice her with fresh hay so it smells super appealing--timothy, or even alfalfa, just to encourage her to eat. You could even try fruit, in small amounts.
If she doesn't eat by about 12 hours, you could (carefully) try syringe-feeding in small amounts. You could mix pellets with water, or even thaw and mush up some frozen blueberries.
Also, make sure to keep them warm. You could run the heat, or even use a hot water bottle (swaddled so they can't chew the rubber). Check their ears to make sure they're not too cold.
How long is your trip, and how far are you going? Trips can be stressful for bunnies. Depending on how your bunnies are with trips, and since you seem prepared to bring them with you, they'll probably be okay if you keep a gentle eye on them--but some bunnies don't handle travel as well as others, so take caution. Also, you might want to remain near enough to go to a vet in case anything flares up, at least for the next five days or so. The first few days after a spay, especially, can be tricky, and I wouldn't want to be unable to call for help if I needed it.
Hopefully that helps. Others will probably be able to pitch in, too, with more helpful information for you. Keep us updated on how they both get on, and I hope they have a speedy, uneventful recovery.