Stray female with kittens.

We found a stray with about 3 day old kittens and have been caring for them the past few days. Since I have cats of my own I have kept mom and kittens in a cage in the garage. She is happy to see me when I check on her, I can pet her, she even let me brush her. She rolled over to show me her belly and I checked all her nipples to make sure they were healthy.
She will come to me and put her paws on my leg if I am sitting, but she does NOT let me pick her up at all.

I want to take her to the vet, but I don't want to scare her or force her while building trust.

Does anyone have advice for getting a stray to the vet and minimizing stress?

You can try and  coach her into a carrier.   Or wrap her up in a thick towel and carry her in into this carrier.   Much better than catch as catch can with sheer force.

But the easiest her is probably to take the kittens into a big carrier, and her after them...  This is probably best too.  She will be very anxious for them otherwise.

Good luck!