Jill,
It's just the beauty of the beast. Adding a nicely engineered set of springs, reducing the center of gravity of the vehicle and stabalizing chassis deflection/strut tower movement will help you reduce that feeling your getting. You are feeling a deflection in the bushings as you brake. It is a heavy car, with a good sized engine and it has room for lateral movement. It only gets "better" with more miles, so whether you put the $ in now or later it's all up to you. I waited until the warranty was up on mine. Then I started to make the modifications.
If you feel it may be an issue with the motor mounts themselves, the driveline/driveshaft "slamming" at the transmission point or that the A/T is producing a "heavy down shift from 1st to Neutral" then you will want to take it in and ask the dealer to test drive it and tell them exactly what you are telling us. Still under 3/36 warranty.
Good luck. Stedda (
www.Stedda.com) is a great company. They and Eibach (
www.Eibach.com) make phenominal product lines for Mustang daily driver applications. It makes our little pony a true engineered machine. Most reputable ASE shops will put in "the big boy parts" for a pretty penny. Sometimes the labor is the most expensive part of the modification. That's unless you have a handfull of buddies and all the right tools to do it yourself (not to mention the handy pneumatic lift in the garage floor)
Hope this helps
Jennifer
aka Jane of all Trades