Your DP is being unreasonable. It’s important to address the needs of both girls!
Many girls are a little chubby at age 11 because that is just before puberty and growth spurt. So try not to worry too much.
Both girls are still growing and will have broadly similar nutritional needs. The aim for most overweight children of your daughter’s age is usually not to lose weight, but to avoid gaining weight while still growing. So basically they should BOTH be eating good nutritionally balanced foods, including snacks, but NOT junk food, so I really don’t see why they should be treated any differently around food - treating them the same will also help promote a healthy attitude about eating for them both.
I think consulting a dietician is a good idea, if you can. Come up with a good, nutritionally balanced programme aimed at maintaining the weight of an 11 year old, and encourage (in so far as you can) the 14 year old to eat the same.
Absolutely discourage talk about who’s fat and who’s thin. I really think in this case treating them both the same is the answer (until and unless you have better guidance from the CAHMS or other medical support team) even if that might sound intuitively wrong. They both have developed (at least slightly) disordered attitudes to food. So they both need to be presented with food that is appropriate for them.
For both girls it is good to normalise eating as a necessary and (hopefully) pleasurable activity, and a time for the family to gather together. Make mealtimes a tiny bit formal (sitting down together, I mean, with food nicely presented, and telephones etc banned for all of you.
I don’t know what the best advice is for serving - my guess is that you should serve, and maybe give your DGD just the tiniest bit more than she thinks she wants (so it doesn’t overwhelm her), and your DD what seems a reasonable portion. But if you can get advice from a dietician they will likely have thoughts on how to handle this.
If you have the time and the energy, eat breakfast together as well.
At meal times, talk to the girls about their day.
You obviously can’t control what happens when your daughter is with her father. The best thing you can do is to try to keep her attitudes about food in your home as healthy as possible, and hope that she eventually takes it in and takes her own control as she matures.
I would not worry too much about DGD effect on your DD, except that it sometimes is the case that anorexic sufferers enjoy feeding others - it’s a way of vicarious eating. So do be careful that DGD is not tempting your daughter to eat extra while starving herself.
This all sounds very difficult for you. Good luck!