Most internal blind systems now are quite good. They will give you that basically total sun control in that case. I would prefer the door to not be a heavily used unit when it is more complex in this case.

Used by whom here? Kids flying in and out of it or adults that could use it more force appropriately?

Most of the Low-e coatings out there (especially one specified for solar control) will give you a very good reduction in glare and radiant energy which might eliminate the needs for a blinds option.