At slow speed one of my front tires on my 2000 Grand Am SE 4 door wobble, but feels fine at a higher rate of speed. Was told by a person at a tire store my tread is breaking loose and I need a new tire. Do you think this is the answer?
You can verify that by looking at the tread and the sidewall. If there is imminent separation, there will be undulation in one or the other. If they're round and straight/linear/curved/however you want to phrase it... no dips or bumps, you're looking at something else. Tire/wheel balance, ball joints, tie rods, etc.
High mileage radial tyres can see the tread bonding cement and/or the internal steel belts loosen. I have seen this with even quality manufacturers such as Goodyear. Once the tyres begin to wear down and approach the tread depth marker, these issues can occur. Poor inflation can also contribute to this.
I have not personally seen a severe tread separation but I have driven on tyres where the belts began to loosen. It happened on all four tyres and the initial indicator was subtle steering vibrations/road following. Even a wheel balance made little difference once this began to occur.
On two of the tyres, looking at the horizontal cross-section, there was an unusual section of an inch or so that was moving outwards. Not something you would see on the around the car tyre check before first drive of the day but evident on closer inspection. The remaining two tyres on the rear exhibited small vibration and then began to show the same characteristic.
Replace your tires.