Weight loss strategy for dog

I've developed some bad habits with my dog that have resulted in her gaining a lot of weight. I was really surprised how much weight she has packed on but I should have realized it was happening. I would like to get the excess weight off of her as quickly as possible but without stressing her out. She has a deformed hind leg from a break that healed on it's own (no I was not in the picture at that point) and I'd like to take pressure off of those joints. She also has a recessed vulva that is getting infected because of the extra weight.

I used to play frisbee with her as a younger dog and stopped because her reactivity was so extreme. I thought that the intense exercise was amplifying her reactivity. I put her on a vacation that has lasted a few years now. She's been on Prozac for a couple of years and I guess that is probably part of the problem as well. I don't think she can manage without the drug however.

She has become accustomed to laying next to me while I eat dinner and I always throw her little morsels of food. Should I taper away from this behavior slowly or feed her something low in calories that will prevent her from getting frustrated. These bad habits started off well intentioned in rewarding a place and relaxed position but have slid into thoughtless patterns.

Even walking is a challenge because triggers will quickly stack and before you know it, her tail is tucked and she can barely respond to me. I'm thinking some activity in the backyard combined with a feeding strategy would work. I'm open to any suggestions. Does anyone have experience in taking weight off of a dog?

Thanks,
Dan