Q: Unless you warm it up for at least 20 min. The car jerks when you first take off.

When we bought the car over 2 years, the previous owners told us she had replaced the transmission twice already. We realized afterwards that it jerked (or bucked?) For the first mile or 2 unless you warm up the car for at least 20 min. (Longer on really cold days).
About a year later the transmission went out again and my late husband (who has always worked on cars and race cars most of his life) , replaced the transmission again. Unfortunately it still didn't fix the jerking or bucking that happens unless you warm it up. Other than that it runs pretty good and it's been a great car for my daughter. It ls jut such a pain when she gets out of work (especially late at night) and she has to sit in the parking lot for more than 20 min. To head home (which is only about 5 miles away). Can you please tell me what you think could be the problem? We would like to get it fixed but don't have a lot of money and don't want to get scammed by any repair person. Thank you!

My car has 200000 miles.
My car has an automatic transmission.