Inline wheels wobble

I have been playing inline hockey for 15+ years but only recently made a switch from goalie to skater. I had not skated on a team since I was about 12 years old. I only play recreationally, so not wanting to spend much money, I found a pair of used skates that seem to be in good condition. However, when taking a sharp turn at high speeds they start to wobble. It is hard to pinpoint where the wobble originates, as sometimes it feels more towards the front and other times towards the middle wheels. I believe it had occurred on both sides. They could stand to be rotated but aren’t terribly imbalanced. Is this an issue of quality with a particular part of the wheels? The chassis? How I am turning? This takes away an advantage of my natural speed, and I would very much like to get to the bottom of this.