we tried it in both, but felt safer doing it in the trailer as she had less room to move around (however we found in the box she just stood there anyway). I think its mainly due to balance. Jazz our mare, used to do it when we set off but also around corners. We used to drive around the block...
I used to have the same problem with my mare... she used to sit down! it been a long process but we have managed to get her travelling. firstly we took the partition out to see if that would help ( it helped slightly as it allowed her to get her balance better). we also thought the problem might...
I have to say i prefer riding on my own. Just being able to spend time with me and my ned is fab! going at whatever speed you want and only have to worry about yourself (that sounds bad!) however I only do it as i know my mare is safe to do so. I wouldnt dream of doing it when my 2 year is...