Dryer wouldn't run more than 15 minutes without blowing the breaker. Thinking we were just running too much stuff, I shut everything down. Still tripped the breaker.

There's two outlets, with dedicated (I assume) outlets, one for the washer and one for the dryer. There's a 15 amp breaker for each in the panel.

I swapped the dryer plug to the washer's outlet and vice versa, and everything works fine. I don't get that at all. The manuals on both spec a dedicated 15-20 amp dedicated line for each.

I'm glad it works, but it bugs me because I can't make sense of it.

Could be a weak breaker, bad outlet, bad connection in a junction box, or loose connection in the power distribution panel.
I'm not a big fan of the type of receptacles that RV manufacturers use. I generally pull them out at the first sign of an issue and replace with a side terminal receptacle. I use a shallow "old work" box where needed

Maybe the original breaker for the Dryer is just marginal and will be fine on the washer, BUT you might want to disconnect all shore power and pull the Power Panel cover and check the tightness on all the wire connections to all the breakers, many have found some quite loose.

Not sure if you have a drier in the slide but check the junction box under the outside where the slide connects to the main body. MANY owners have found poor connections from the romex to the black cord. A loose burned connection will cause a breakers to tip with a heavy load

Mine's in the closet all the way up front, but thanks for the heads up.

Maybe the original breaker for the Dryer is just marginal and will be fine on the washer, BUT you might want to disconnect all shore power and pull the Power Panel cover and check the tightness on all the wire connections to all the breakers, many have found some quite loose.

That's good to know. I have to move in a few days I'll do it then. The receptacles will be harder to check. I'll have to dismount the dryer.