Engine shutters in park or at stop light

More info please ! Steering wheel wont shake in park if vehicle not moving. But to hazard a guess without knowing make year are model would not be possible .

You should have diagnosed & found a problem,
BEFORE you did the alignment, because now if
you find you need parts, to solve the problem,you
may have to align it again & now you may also be
wearing the new tires

Wrong strategy & I assume wrong shop, or they didn't
understand or care what your vehicles issues were

People seem to always think an alignment will solve
mechanical issues, for some reason

For me-- I ask,why does a fairly new 2008 vehicle have those
problems in the first place?

have a wheel alignment dine ( back first then front ) as it indicates a castor wobble
could be wheel bearings , tie rod ends or suspension rubber mounts

if you let off the gas and it stops vibrating, have the cv axles checked. if the steering wheel shakes at parking lot speeds, a tire is bad.

check for broken engine support, bushings of shocks and chassis all of that is concern with viration...

Your disc brake rotors are warped. Solution? Remove the disc brake rotors and have them turned on a brake lathe. Warpage comes from a hot disc brake rotor going through a puddle of water which causes the warpage. If you have a Parking Brake, get in a safe area and when stopping, ONLY apply the parking brake. If the steering wheel stops shaking...there's your problem...warped disc brake rotors.

Try to get the front wheels balanced.

when slowing to make right turn is it more like a clicking noise, does it do it while turning or just when slowing down. If it is while you are turning it is most likely the right cv axle drive shaft popping. When at a stop with ac on does it shake if you put it in park and how do the rpms read in park or in drive. Did they change the trans mount also dont thank that is it just trying to get a better understanding so I can better assist you.

try taking the vehicle out in the parking lot and cut the wheel to hard lock, apply light throttle and do circles to the left, stop cut the wheel to hard lock on the other side and repeat this three or four times, also you can apply throttle while in park and rotate steering wheel lock to lock many times, the explorers are known for having air trapped in lines,try this and let me know.

This is usually caused from air in the power steering system. On more then one occasion i've experienced this after doing a brake job or an alignment. Because you turn the wheels with out the engine running you move power steering fluid throughout the system aerating it. The fix is to simply turn the wheel lock to lock repeatedly with the engine on and parked. This will "bleed" the system. Oddly Explorers are the only vehicle i've ever seen this happen to. Unfortunately it looks like you replaced the wheel bearing needlessly.