I find that the cane varieties and wax begonias (semperflorens) can take full sun as long as they do not dry out. Rhizomatous can as well but I feel like they appreciate the shade during the late afternoon (after 2 PM until 6 PM in summer hours). Rexes probably like it like rhizomatous do - a mix of sun in morning, late evening; but partial shade during the heat of the day.
Some of the terrarium type begonias probably need less light than their brethren though. I keep my terrariums indoors under lights year round.
I would play around with different scenarios if you have the time and energy to relocate pots around the two shade houses.
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Clarifies the matter
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