Is it possible to move around during combat?
Solution 1:
It's been a long time since I played Chrono Trigger on the DS, but I don't recall anyway to do so. The only thing to try is to use the DS-style input controls (I recall there being two input modes, one more like the SNES original, and a newer one with more touch controls). If there is a way, it would be when using the new control style.
I still don't think that you can move your party members around, unfortunately.
Solution 2:
No, there is no way to purposefully move your characters in the SNES or DS versions of Chrono Trigger. Each individual fight seems to start with set locations for where your characters stand.
This does mean a few fights (not many) have certain party configurations that are better than others due to positioning. In particular, I recall the final boss battle has a pretty fun combo attack with 2 characters if one of them is in a particular spot.
(In case you care, the one I liked was Lucca and Robo with Robo in the 3rd party slot. Robo ends up with a great dual attack with Lucca that had a powerful AoE around him, which was important because the boss was near enough to him to be hit by it.)