I need some advice for these car problems that I'm having:
1) First issue: I drive a 2000 dodge neon, automatic, my car vibrates hard when I slow down and get to about 20mph. It seems like its the transmission. It seems like its having a problem going back into first or second gear from a higher gear.
2) Second issue: My tire psi keeps going up and down by about 5psi. Is it because I have economy tires or is it do to temperature change.

 

When the tires are hot the pressure increases and when it cools off it drops.And the first problem is solved by getting rid of the neon J/K could be many things,bad tie rod,bent rim(maybe) bad cv shaft or a bad tranny (maybe the converter) its hard to give you an answer without you telling us a more directed area were the shake is coming from.Does the car shake or the wheel shake or what??

 

Probally a broke motor mount somewhere,again FWD cars are notourious for breaking motor mounts and that is also normal with the tire pressure like he stated above,the hotter the air the more pressure it will produce inside the tire and the colder the less pressure.

 

if the steering wheel shakes then you probably have bent/warped rotors or uneven wear on brake pads. if the car shakes then there could be many things as stated by 99saleen351r

 

It'll also shake at slow speeds while going up a steep hill, what might be the problem with that situation, the tranny?