It sounds like you're doing a fantastic job training him yourself! It was my understanding after attending a training course, that it's more a course to teach
you how to train your dog. If you're doing well right now, it may not be horrible to just continue on as you are. I don't think all dogs need to go to 'puppy training schools'.
I can relate to your dog not being food-motivated. Scottie wasn't either at first. That was the main reason I had a slow start to training him when I got him at 5 months. He wasn't toy-motivated either.
When I finally got a clicker, persistently did my 10-15 minute daily training sessions with him (a few times throughout the day) and he showed the slightest bit of progress, I was so thrilled! I think my excitement showed and he fed off of that. My genuine excitement was his motivation and he started to enjoy the training/bonding with me! It was really funny when I learned how my excitement translated to his excitement lol...it was a lot of "What a goood boy!! You're the smartest!! You're the best boy ever!!"
From then onward, because he had a sensitive stomach, I trained him with his kibble and a clicker. As long as he was hungry, he was willing to learn.
After he got his basics (and then I had to 'train' him how to eat his meals without me feeding him), I started using treats when he was about 1 yr old. Instead of liver, which can cause upset stomach if fed too much, try lamb lung! Don't quote me on it, but I read that it can be fed as a protein. At the very least, my mister-most-sensitive-dog-ever Scottie didn't get upset stomach from it. In addition, green tripe is a very smelly but tasty treat almost all dogs cannot resist. You can buy it in the dehydrated 'whole' form or the freeze-dried pellet form.
Scottie was also 'like a cat'. He is quite an independent individual. He wasn't really a lap dog at first. But slowly and gradually, he became more cuddly. I think I had to accept that, because I didn't grant him access to the couch, as I wanted to train him he wasn't allowed on-off access at his will, but only on my terms (my fear is that he'll hurt himself jumping on and off). I was really strict! But I think I had to be, because boy, he's too smart for his own good and tries so hard many times to 'own me'. It's a battle really...but I insist on being 'boss'/'pack leader'.
At 9 months, I'd say you're doing good. Just be consistent with training the 'come' command. Treat every time he comes. Keep treats with you in all your pockets, so he doesn't know when you have it and when you don't. Make sure it's always fun when he comes (and never ever anything bad when he comes).
If you're concerned with being counter-productive, have you seen some Youtube videos on training? I am a fan of Kikopup's channel. Check it out:
https://www.youtube.com/watch?v=tV5qsH5tjYA Not sure what your trainer's style is, but I think whatever style you go with and the dog picks up on it, it's a good style
I've also come to terms that Scottie may never get 'come' down 100%. He's a toy breed; they're too mischievous and fun-loving to be that reliable. I just make sure I protect him at all times from any possible dangers. I occasionally get envious of those who walk/play with their dogs off-leash in public. But I also think, because he's so small and precious, I'd rather be protective of him than to risk him being hurt either by another dog or by traffic (you just never know!). I also recommend to not use the retractable leash, many others warned about using it. One story went on to be as crazy as the retractable wire slicing off the guys' finger and him not even realizing it!
Anyway, it's up to you, but I use a leather leash which gives me easy control and it's easy on the hand.
Best wishes to your daughter for the lung transplant. I love this forum as well, it's such a great tight-knit community.