I just go with the flow. I understand what your saying though. Recently went on a trip and it was supposed to be good weather...then the day before it changed to "isolated" rain for 2 of 4 days we would be there. Well the rain came in the second night and most of the third day. We still had fun, still had a couple campfires, and the mud really wasn't that bad, but it wasn't heavy rain...just a light constant rain.
I was very surprised to see how well our outdoor rug did in the weather as some of it was exposed outside the awning, and part of it was being dumped on by the awning. Day 4 when I packed eveything up, it was hardly damp, if at all, and little mug on it, despite being on ground that was more dirt and less grass.
The baby will be fine, it might not know any difference if you had to be in the rig all day. :) The dog will love the weather, you just may want to be more vigilant in cleaning him/her up before going back into the rig.
That said, if its calling for flooding thunder showers all weekend and I call late and can't get a refund or a date change, I'm probably just sucking it up and eating the bill. :)