1999 Dodge Intrepid help!

Did you tell the mechanic about the shaking when you took it in for an alignment? If he was not aware of it, he may have not test-driven it fast enough to check for that.

A broken belt in a tire will cause a wobble. Worn tie rod ends will not cause a shaking, but they can aggravate a shaking caused by something else. Both of these should have been inspected before an alignment was performed. Another possibility is a bent wheel, but you should feel that at almost any speed. Rattling anti-sway bar links are extremely common on this car but they won't cause a wobble either.

Take the car back to the same shop because they will warranty their work. If they find the cause of the shaking, you can legitimately be expected to pay for additional parts and labor, but they should re-align the car for no charge. As a point of interest, all modern alignment equipment is designed to account for and overlook a bent wheel during the setup process, so the alignment can still be correct after replacing the wheel. Replacing worn parts that hold the wheel and steering parts in place, however, will require a re-alignment.

If necessary, go with the mechanic on a test drive to be certain he sees the problem. If it doesn't act up all the time, make mental notes about when it does occur. Things like rough roads, wet roads, only after the engine is warmed up, etc. Can provide clues. You already found one clue; over 40 mph.

Caradiodoc

Have them check tires and tire balance
and I see it very difficult to do an alignment with bad tie rod
and they should advised you on getting it fixed 1st
since you know that tie rod bad should have them replaced as it is your safety