Ok, heres what I would think about. Lets say your mom bought you a horse(not a suggestion at all) and your horse started acting like Kelly would you give up on her? Would you dump her? No (atleast I'd hope not) you would want to make your partnership as good as possible and work on the issues. Do that with Kelly, you may find she is the best horse at the barn. Oh and think how good you will look when(because you will do it if you put everything into it) you show everyone how awesome your mount is.
Yup, for me there's nothing more motivating than people saying "Oh, that horse is so difficult/unpredictable/stubborn" or "Why not just sell him and get something fun to ride?" - got that second one a lot with Brock. There were many times when I'd be found having a good cry in the tackroom after a bad session. But the more people said "you just don't seem to be having fun" or "wouldn't you like a horse that's ready to compete?", the more determined I became to overcome the problems. I knew I wasn't overfaced with him, it was just such a wide range of problems and the lazy bit of me just wanted to hop on and ride like I would on a finished horse, and concentrate on my riding.
But riding Brock did more for my riding skills than any lesson horse ever did - my seat is 1000% better, my confidence is sky-high and I've learned a lot of patience and how to problem-solve on the go. No well-behaved push-button horse could have ever taught me that stuff. And people saw me ride and remembered what he was like when I first got him, and remarked that we'd come a long way. That was nice, but the best feeling came from when I'd realise we'd just done something without even thinking that we couldn't do at all 3-6 months before. That was real payoff for all the blood, sweat, dirt, tears, bruises and replacement helmets.
Keep persevering with Kelly (if you can't change instructors) - but do try and ride Gray Guy occasionally, even if it means getting a separate additional lesson. It's sometimes good to check your progress on an easier horse, and I think you'll quickly find as you progress with Kelly that riding horses like Gray Guy is pretty boring (no offence to them - they have an important job!). I can't even go on a trail or hack anymore without asking for a horse with spooking/bolting issues - I need something
to keep me entertained
and you will too. Just keep reminding yourself you'll be a much better rider at the end of it all, and tick off each thing you can do with Kelly as you do them (start off with simple stuff like "an energetic walk" or "cantering" but then move onto more difficult stuff like "canter at the first ask", "halt with seat only", "well-shaped small circle at trot" etc). It's a great way to feel like you're actually getting somewhere!