With her bad leg, I'd be cautious about high-impact exercises, as those can be hard on even healthy joints. These include things like running/biking with the dog on a hard surface like asphalt, anything involving repeated jumping (like catching a frisbee in the air or agility hurdles), and having the dog go up and down stairs excessively. These might be okay with her, but you'll want to clear it with her vet, veterinary chiropractor, or canine rehab specialist who can evaluate her current condition and determine what's safe for her leg.
Generally speaking, low-impact exercise like wading and swimming is excellent for weight loss! You could also try taking part of her daily meal allowance and hiding it around the yard, so she has to move and sniff for it to eat. This does triple duty, because it's gentle activity, but it also engages her brain and promotes sniffing, which is a naturally calming behavior in dogs. Slow and steady is definitely the way to go - just like with humans, fast weight loss can be dangerous.
Definitely follow up on checking her thyroid, especially if you don't see changes in her weight even with a change in diet and lifestyle. I totally understand it being difficult with her being so stressed at the vet's, but as Shell said, reasonable diet and exercise adjustments shouldn't be harmful in the meantime if you can't get her in right away.
Generally speaking, low-impact exercise like wading and swimming is excellent for weight loss! You could also try taking part of her daily meal allowance and hiding it around the yard, so she has to move and sniff for it to eat. This does triple duty, because it's gentle activity, but it also engages her brain and promotes sniffing, which is a naturally calming behavior in dogs. Slow and steady is definitely the way to go - just like with humans, fast weight loss can be dangerous.
Definitely follow up on checking her thyroid, especially if you don't see changes in her weight even with a change in diet and lifestyle. I totally understand it being difficult with her being so stressed at the vet's, but as Shell said, reasonable diet and exercise adjustments shouldn't be harmful in the meantime if you can't get her in right away.
