Then switched the registration of another car (originally registered in Utah) to Texas, again with a Utah DL.

I don't think it matters. They'll take your money and register the car wherever it is.

By the way, I'd be hesitant to switch to a Utah DL. I guess it depends on what your daughter wants to claim as her "residence" but if she wants to claim that CA residency with you (in spite of the fact that she's attending school in Utah) she's well within her rights and the contours of the law to do so.