Oh Goodness, your poor little girl!
We once got a rescue in that was just like your little girl and we knew that if we didn't get the weight off and fast the future looked pretty dim for chewy.
This is the diet we used:
People don't know how to get their dogs to lose weight without all the side effects - begging, that sad-eyed look that says "I'm hungry", etc.
(This was written for a large dog from the vet website I got this but I am sure you get the idea.) Try the pumpkin diet. Reduce your dog's regular food by 33% and replace it with a 67% volume of canned pumpkin (not the kind with sugar and spices, ready-made for pies). For example, if you are currently feeding your dog 3 cups of food, you would instead feed him 2 cups of food and a whole cup of canned pumpkin. Dogs love the pumpkin - it has the texture of canned dog food, it provides vitamins and roughage, it makes them feel full (so they don't forage in the yard for leftovers), and they lose weight!
We completely left out the dry food and replaced it with cut up green beans and made sure Chewy had vitamins. The only treats he got were Charlie Bears and then only a few a day. Then 2x's a day he was taken for a walk even if at first he didn't want to. It was hard for him because of the weight and the stress that was put on his heart but either we did this or he would die very young - just like human's that are obese. It took about 3 months to get his weight off but what a difference in his attitude as the pounds started coming off. He got more energy and started to play. It really was a joy to watch and today he is with his adoptive family that says he is a beautiful svelte puppy (even though he is 7 years old)
I know this will be hard for you but just remember the mother saying "this is going to hurt me more than you" because I know you love your girl and want her to live a long and healthy life.
Good Luck