So the remote start turns the engine over after 2 seconds and the starter drags when it does this?

What brand of Remote Start do you have?

Since you had it installed, take it back to the installer and let them know of your concerns.

As for riding smoother, get new struts, sway bar end links (F&R), front sway bar center bushings, better trailing arms, good balance and rotate. Proper air pressure in tires.

For going faster look up the safely modding your 3800 Thread as mentioned above.