What's my crutch? Do you mean my core? I'm very much a beginner (maybe 15 hours in the saddle), and only now am I finally able to commit to weekly lessons, so I know I'm still a bit tense. I don't feel any pain when I'm doing the sitting trot (so therefore I'm not thinking about it), the stiffness usually sets in on the long car ride home. Perhaps I need to stretch before and after my ride - would that help, in addition to relaxing and doing other cross-training exercises?
So far I've only been sitting the trot in my transitions and I'm still getting the hang of my diagonals. I don't do it for extended periods of time, so at this point, I don't know how much I need it or what my instructor has in store for me down the road. The horse I ride is pretty awesome, and I don't think he's the problem - it's all me! My instructor is amazing (very well accomplished) and she is always reminding me to relax in order to smooth out my transitions, but I haven't mentioned the stiffness to her yet. I will at our next lesson on Saturday.
And like I said, it's not full-blown pain I'm feeling. Just muscular stiffness/tenderness that restricts my mobility for a day or two afterwards. So I'm not worried about it per se, but I do want to correct it so that I don't have any problems down the road.
Maybe this is a good excuse to start getting massages.