Nothing wrong... just sounds like an territorial female rabbit. Honestly, at this point I don't think you're going to make her enjoy being picked up before the vet visit, so instead you might want to make each handling session as short and unobtrusive for her as possible. If she is back into a corner facing you it should be pretty easy to pick her up. Remember - rabbits can't move their head upwards as easily as they can move it from side to side, so reach in your hand QUICKLY over the rabbits head and grab the base of her ears (preferably with your non-dominant hand - I usually like to have one ear in between my index and middle finger, and the other in between my middle and ring finger. The palm of your hand should be pressed flat against her forehead - you want your hand as low on the ear base as possible, so that if the rabbit were to try to pull away you won't be pulling the ears - and hold tight so she doesn't slip out). Once you have control of her ear base, you have control of her head, so she can't spin around and bite you. Use your other hand to reach under her and pick her up or slide her towards your body. All her weight should be on the hand that's under her body - you never want to put weight or pressure on the ears. Once you have her out of the hutch, tuck her head in your armpit and carry her like a football.
As a judge I have to deal with getting many, many aggressive rabbits out of cages and this is what I've found to be the safest for the rabbit, and the easiest for me - however it's much easier to have somebody show you than to try to describe it here - it's hard to emphasize in text how you are not putting any of the rabbit's weight on the ears (as the ears themselves are delicate), but rather gaining control by preventing the rabbit from moving its head from side to side.