steering issue that corrects it self durring accleration

i have a 96 Geo metro 1.3l that my wife bought off her friend for $700 with out me inspecting first. when driving slow the steering wheel is approximately 45 degrees off set and drives almost straight, but stepping on the gas and accelerating i feel the the steering wheel straighten out (like the drive wheel is kinda dragging with out power) and drives almost straight pulls to the left slightly. i checked the air in tires and did a quick visual under the car and found a broken passenger side stabilizer link that seems to have been broken for a long time i will place an order for a weekend repair. when parked i don't seem to feel any play and slight movement of the wheel give a slight movement of the tire. i also don't seem to feel any play in the wheels while on the ground and will recheck for play while in the air this weekend. also the last owner put slightly wider tires on the car but i didn't notice this issue when we got the car/ though it may have been there and something happened that i ended up realizing it was happening. what else should i be checking or is it just in a need for an alignment and the stabilizer replaced

side note not related to issue this car only has 111234 miles on it and other than a rusty bottom and holes in the rocker panel i improperly slapped bondo onto till its warm enough to properly fix it runs great and would like to get another yr or 2 till i can afford to get a newer car. this site requred a pictuire but thats not my car just the exact model for reference

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go to a good alignment shop, start there. Pray that's off and steering wheel needs centering, those guys can do that. Just don't put much money into that thing, they were pretty junky cars. The prisms were pretty good, but not the metros