Dodge Caravan pulls right when shifting

Good day, everyone. I have been a reader for years and finally have a problem worthy of your consideration. I recently acquired my brother-in-law’s old 2000 Dodge Grand Caravan. It has over 200,000 miles on it, so I am not inclined to spend much on repairs. It has an automatic transmission which runs well, but pulls distinctly to the right when it shifts gears. The effect is strongest when it goes for 2nd to 3rd, but it is noticeable at other gears. It does not pull when it is running normally. Tires are new and looks to be balanced and aligned. Likewise, the brakes seem ok. First, what do you think is going on? And, second, is it dangerous to drive it in this condition and will it get worse if unattended?

Thanks for your advice.

Could be normal if it is torque steer. If the front and left drive shaft are not symmetrical, some engine induced steering occurs. Most noticed when the transmission shifts or the engine rpm is raised. Maybe see if another one like it does the same thing. Any damage to the drive shafts which causes even greater non-symmetry would of course aggravate this.

You might also check the ball joints as a worn ball joint can be very dangerous if one of them decides to give way.

Also have the engine/transaxle craddle mounts inspected.

Tester

My '88 Accord once had a sudden increase in torque steer, at 13 years old.
A few hundred miles later the dry ball joint started to squeak.
I promptly replaced all 6 (4 front, 2 rear).