Floating brakes

For a week I have been reading about the phenomenon of fluttering while braking. It seems that there are many reasons for this. I can exclude drawn brake discs and rented chassis parts. I have a winter tyre set with a maximum of 3mm profile on it, even a few years old. Up to 110 kmh it vibrates easily on the steering wheel, after that strong braking. An imbalance with wheels is only noticeable at a certain speed range. s the flatter problem after changing to new wheels away is fixed? I will have to drive on these wheels for about a month but the topic is already wurming me. Has anyone had a similar experience with their brakes? LG