I wouldn't recommend removing the fat baby, as with only two kits, mom should have plenty of milk to go around. I would try and hold the wrinkled kit up under her belly(carefully so it doesn't get kicked by the doe) while the doe is either being held gently but securely or while she is distracted.
You could try now or you may have to time it so it's not after she just nursed, but closer to the time when she's ready to nurse so her milk is full. You will likely have to hold the baby there for a while though, like maybe even up to 20 minutes. Sometimes trying to feed them off schedule the baby takes longer to fill up. You can tell by watching for the white patch on the kits belly to indicate the stomach is full of milk.
Though with there only being two kits, she should have plenty of milk to go around. So either her milk hasn't fully come in, she's not producing enough, or there could be a medical issue with the baby. Aside from trying to get the baby in for supplemental feeds, about all you can do is make sure the doe has lots of food and keep an eye on the baby.
Nursing does need lots of extra food themselves, to keep those babies supplied with milk. So free fed grass hay(eating at least a pile the size of her body per day, and continuing to produce healthy poops), some alfalfa if you want, and unlimited or close to unlimited of pellets, then whatever veg/greens you normally feed. If she is on a low protein grass based pellet, you will need to start to gradually transition her to a higher protein alfalfa based junior pellet, and in the meantime I would start supplementing with alfalfa hay until that transition is made and she is getting close to unlimited junior pellets. Alfalfa and junior pellets are higher in protein and calcium, which is what a nursing doe needs.
Here's a guide on taking care of mom and an accidental litter.
https://flashsplace.webs.com/accidentallitters.htm
