Around here, nobody seems to mess with my bike trailer, although I suppose there is a first time for everything. I've had a few bike lights stolen. I've seen people lock up the trailers with a really long cable lock. I do several stops in a day, but there are some things I won't leave in a trailer including computers.

I'm not sure how stores would react to taking them inside. If they're relatively empty, and clean, then they might not care. I presume the Travoy would be easy to take inside.

Another option might be to look at a trailer + stroller attachment.