Oh, dear....this subject ranks right up there with tire choices. And, true, it's been around the block a zillion times with probably 90%+ feeling that it's a bad idea. I'm included in that 90%. I would not put our pups in the trailer for several reasons....getting sick is one reason, you can't see what's actually going on back there, it may be more stressful for them than you'd imagine. The legal issue has been passed around and I can't recall what, if any, the thought was on that. To have people in the trailer when underway is against the law, but not sure about pets.
Re the horse/horse trailer issue....horse trailers are designed to carry horses, while TT are not designed to carry any living thing while traveling. This is one of those times that a Class C or A would sure be a benefit. So, my answer is no, do not carry your dogs in the TT, even accounting for the inconvenience in potty breaks. Sorry.