Is there a word like "ambidextrous" to describe mixed hemisphere brain dominance?

It really is an interesting question. While the left/right brain distinction is being disputed somewhat within psychology (in terms of each hemisphere being the domain of a certain type of abilities mostly absent in its opposite), whenever there is discussion on this topic it practically never features the idea that the two can be equally dominant. That option is not denied, it's just never discussed for long enough to give us a term to go by.

I have been able to find one term that might describe what you're looking for though: hemispheric synchronization.

It is a bit of a mouth-full, admittedly. You might also be able to use symmetry, and I have also seen the term bilateral being used.

This questionnaire will give you an indication of your tendency to be a left-brain learner, a right-brain learner, or a bilateral learner (using both about equally).

I've also encountered the term bilateral symmetry used together.

The hemispheres exhibit strong, but not complete, bilateral symmetry in both structure and function.

tl;dr:

• hemispheric synchronization
• bilateral/bilaterality
• bilateral symmetry