Should I get another coach for private lessons?

I’ve been figure skating for almost three months now. Three weeks in I began skating about at least three/four hours a week. I know it’s not too much and that I haven’t been skating for that long, but I feel like I could’ve been better by now. Especially compared to what I see beginners of my age (20) do in just one year. Today I had a skilled figure skater help me out with some crossovers. He told me to do things differently and held me a bit when I first tried it out his way. It felt so smooth and correct. I never really had that with my current trainer. It’s always still a bit wobbly when he tries to hold me whilst teaching me certain things. It was like a switch turned inside of my head and my body did the right thing. Even when I tried it out more on my own, I understood why and how I had to do it that way. I was kind of blown away by this. He taught me things more in depth and in a way that was easy for me to copy. It felt natural. He sadly doesn’t teach, but I’d like to get some private lessons with a coach that can work with me like he did. I don’t feel like my current coach from my group lessons could do it. Although I might just try private lessons out with him anyway. I’m strongly thinking about searching for a good coach for me personally. I met one on the ice today, but he’s in a fight with my current coach. So I guess that would be a bit of a shitty move from me. Do I really have to worry about getting another coach though? Is it really not done to try the other ‘rival’ coach out? How have you guys met the right coach? There’s not much out here on the internet about local clubs. (Yes, I tried. Hard…) Is it purely a matter of asking around on the ice?