I second trying in the football hold for the side she doesn't like. I would 'trick' DD by doing this and then switching to the cradle hold once she thought she'd had enough. Since she persisted a bit more in the football hold and let down had happened she was often happier to stay on the slower side.

Have you considered taking her to a paed chiro? She may not like turning her head that way or staying in that position for a reason.