She is SO cute!!!!!!!!!!!!!!!!!!!!!!!!!
How far is the closest vet? I would definitely call them to see about having her (or however many of them!) spayed on the way home. When they spay kitties, if they do it in the morning, some places let you pick them up in the afternoon - other places have them spend the night. In this case, if they can be groggy for the rest of the car ride home, that's probably a good idea.
That said - it's best not to spay a kitty until her kittens are weaned. If someone had seen a kitten, then they're probably already weaned, or old enough to be (they can be weaned at 3 - 4 weeks, though moms will let them nurse longer even though they can eat regular food).
What else to bring?
A thick garbage bag or light tarp to cover your seats where you will set the trap. They may be scared and eliminate anything in their systems.
A couple rolls of paper towels.
To help the trapping, pouring litter over the bottom of the trap or a bunch of loose soil so the traps lift up through them but the kitties don't have to feel wire on their feet will help.
If the traps can be washed (get the scent of fear off of them) before you put them out, that will help.
I'd purchase Feliway spray. It is a synthetic hormone that mimics the friendly markers in cats' cheeks. This may help calm them a little. You don't spray it on the cats - you spray a little on the wires at the edge of the traps - and before you transport, maybe on the back of the seats where the traps will be.
I'd be prepared at home to have them if you're able to trap them! Make sure your apartment is "cat proofed" - no way to get out, no openings in walls or ceilings they can hide in, etc.
It's best to release them into one room at first. Cats are territorial, so when changing their territory, it's easiest for them to transition with a smaller territory that they make their own before worrying about them having access to the whole apartment.
Under the bed works great as a "safe" space - but maybe put a couple of slightly larger than cat-sized boxes out on their sides for them to have "hidey" spaces.
I know it will be a major bummer if you're not able to trap them, but you really ought to have litter boxes and food/water &etc. ready for them. And you can use the Feliway spray you bring up with you in their room.
Food is a great motivator when socializing - might want to have some meat baby food handy (chicken, beef, or lamb is best - just plain meat, make sure it has no garlic or onion powder in it - we use Gerbers).
You may want to have leather gloves with a long sleeve on them just in case you have to grab kitties by hand. They can turn into little hellions when handling them (if you're trying to get them into a crate).
I don't know how much space you have in your car/truck - but if there's room for a couple of largish crates, you may want to bring those. If you're able to get them spayed on the way home, it will be much more comfortable for them to be in crates when the vets return them to you rather than putting them back in the traps.
I'll see if I think of anything else. I'm sure others will have suggestions.
I'm so excited you're going to try!