Do you have any family or friends that could possibly keep them? I could never keep my dogs outside all the time. Especially my Yorkie. He is so small and gets so cold even when I take him outside in the mornings and evening. What about a pet-friendly hotel? Some hotels have reduced rates for extended stays. Has your friend with the RV met and observed your dogs personally? If she sees how well-behaved they are, she might change her mind.
If your only two options are truly outside versus boarding, I think I might feel more comfortable boarding them overnight. Is there a way you could take them to the boarding facility in the evening and pick them up each morning? This way they aren't spending all of their time outside, but get to sleep somewhere warm. Plus they won't have to spend 2-3 weeks in a kennel without seeing you.
__________________ katy&levi 
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