1998 Mercury Sable Tire problems

After driving more than 10-15 minutes or even less if I'm driving at a higher speed, my car heavily vibrates when slowing down to stop. It's a scary feeling. The breaks are fine and the car otherwise is in very good condition. Also, after I come to a complete stop the vibration discontinues for a little while.

I took my vehicle to the dealer and had a belt plus all the tires replaced because I was told a tire was seperating from the vehicle which was causing the problem.

Afterwards, even though the car didn't feel like it was falling apart like before, it was still vibrating pretty heavily so I took it back to the dealer but they said they could not find anything wrong. We drove around town but because we made frequent stops along the way the car behaved normally. I was embarrassed.

I then took my vehicle to a local tire shop and asked them to balance and rotate the tires as suggested by a friend. They were slightly out of balance but it didn't fix my problem. I'm to nervous to drive my car any further than just going to work and my kids don't want to ride in the car.

Are there any visible problems or signs I could check for myself before I take it back?