When I am going about 60 miles per hour the car doesn't run smooth, feels shakey. My tires were replaced in the front about 6 months ago.

all machines vibrate.
only some too much.
and the car has over 3000 parts that can vibrated, for sure loose.
find tire shop
and ask them to check tires for balance.
that was a wild useless guess,,
i cant drive your car, and feel and hear it vib
so find live human to do that.
go to any shop in town, and ask for help
and win.

This is usually caused by the rims being out of balance go to a tire shop and have them balance the rims. Hope this helps you

run the fault codes and look for problem cam or crank position sensor
could be a problem engine mount that is being started by a misfire

Don't think it's missing. Low fuel. Check fuel pressure after regulator.

The following is the scheduled mainainence per Chrysler at 60,000 miles:

1. Change engine oil & filter
2. Air cleaner filters
3. Rotate tires
4. Check spare tire pressure & stowage
5. Change automatic transaxle fluid & filter
6. Engine coolant flush (every 60 months or 102,000 mile whichever comes first)

I hope this helped and good luck

Hoses about every 6 years, Belts every 30k And if its that clean, Drive it and make sure it shifts out ok warm and hot, Get it up to 50-60 mph with all sounds off and listen for a whine even a slight wine, If none heard id say buy it, The whine i spoke of is rear diff noise by the way.

check front tire and then struts

Let me see know at 45 miles per hour a vehicle usually shifts gears into the highest gear so could it be the torque converter hanging up and not shifting quick enough or maybe its the U joints. Have the transmission fluid checked for proper level and color.
Here's a small test for you when your accelerating up to 55 miles per hour try letting off the pedal at 44 miles per hour and then reaccelerating up to the 55 mph and tell me if it`s smoother if it is then chances are that it`s hang up on third gear. There's also a electric sensor located on transmission that assist shifting it`s usually controlled by the engine timing.
One more thing did the repair man check to see if the tires where directional tires if there not put on right it could cause vibration and early wear out .Hope i helped you.

This is Caused by an Out of alignment Front end. Get the Front end Alligned and your Problem should go away.

its going to be in the alignment...have the front end realigned