The glucosamine is probably what's causing her itching; it's a well-known and fairly common side effect (in both dogs and humans). Friend put her dog on it and he itched so bad that he got to where he was pulling bloody chunks out of his hide, and gnawing on his feet. Took him off it and the problem went away. As to whether it helps joint issues, the research is at best inconclusive. And dogs may not know placebos, but they will react to human expectations.
Here's where I should remark that I used to manufacture custom dog food for my kennel (don't now cuz I can get near-enough off the shelf)... based on biochemical research (I went to university in biochem), not the weird ideas all over the net.
That's probably a decent diet (red meat, lots of protein and fat -- which is why she feels satisfied enough to be a nibbler; not too much fibre) but as a FYI:
Grain-free is not necessarily a good idea. The wild diet of small rodents includes the digestive contents, and what might those be? Largely seeds and grain in a 'cooked' (digested) form, roughly 30% by weight. There's been some interesting research on grain-based vs grain-free in working sled dogs, and the result was... on a grain-free diet, they simply can't get enough calories, and starvation became an issue. -- Know what the Fish & Game dept. uses to rehab the starving wolves they pick up every winter? Purina Dog Chow.
The salmon oil and/or sweet potatoes are probably causing the belching, but I'd bet on the salmon oil. -- Rosemary is a gastric irritant, but far as I can tell no one puts enough in any diet to irritate the gut; it's mostly there to look good on the label.
The problem with taking weight off the dog for bad hips (other than when they're obese) is that a large proportion of the lost weight will be muscle and connective tissue, which can make the joints more unstable than before, and therefore more painful (if she has pain -- most dogs with bad hips don't even notice it). She'll be best off when she's in good normal flesh, ribs well-covered (no 'dents' between the ribs, and definitely none along the backbone) but not mushy. Also, she'll age better than if she's thin.
I've found the best approach for mungy ears is washing 'em out with plain water
every day without fail -- it can take six months or more but this usually gets rid of the problem (unless there's an autoimmune issue at work, in which case you do it for life). I know folks who've used contact lens solution with good results. Probably just doing the mechanical cleaning every day, regardless of what you use, is the real trick.
BTW I've raised over 2500 dogs across 45 years (current average healthy lifespan is 14 years), including 59 show champions plus a number of working titles... here's one of 'em:
And this is the conversation I've repeatedly had at shows:
Them: Your dogs are always in such good condition and their coats are great. I wish my dogs looked half that good. Whatever are you feeding? What do you put on their coats??
Me: cheapo grocery brand, and absolutely nothing on the coat.
Them: OMG, I could never feed that, how horrible!
Me: You just got done telling me how my dogs look so much better than yours, so what's the problem??