Have a 01 dmax. When you stop say at a light or stop sign even from shifting from park to drive and you step on it I'll fill to thumps I think from the tranny. Kind of feels like the tranny slipping and then catches and goes.

have you changed the tranny spinon filter,and ck the fluid level

There is a service calibration fix for this delayed 2-1 downshift.

the 2001 trucks have a odd problem if you coast to a stop without useing the brake the trans stays in second untill it moves a inch or so then it disconnects , down shift and takes off in first . Does this sond like whats going on? It would happen mostly slowing to a stop on a steep hill without using the brakes.