I think it all comes down to communication... as mentioned earlier... Gabby is learning human vocabulary, and the humans (and kids) are learning Puppy vocabulary. It's a process.
Sounds like you're both learning.
I learn more with every puppy we work with, too.
Since Gabby is reacting badly to being picked up, I'd be working a LOT on calm touching... playing with her feet, rubbing her belly (which she seems to like), pulling her ears (gently), then rubbing them (all my dogs LOVE to have ear rubs)... do all the things you might expect the vet to need to do at the next vet visit (i.e. pick up and look under her tail, rub the base of her tail, feel up along her spine, count her ribs, rub all her feet, play with her toes, look in her ears, open her mouth, check her teeth, etc, etc,) and do this as play time and relaxation time, so it's comfortable. Find her "limits"... and work up to them - don't shove her out of her comfort zone (and stop when she asks... i.e. with the growl) - work on expanding her trust and ability to remain calm when being poked and prodded.
Some of my favorite human vocabulary words to teach early are "gentle", "relax" and "wait".
If she already knows "place" you're doing a great job!