Welcome!
Its wonderful to see some younger people joining the forum. We need young families to be part of our community.
As far as traveling with dogs, we traveled through WA, MT, WY, and into SD with our German Shepherd last summer. We also have a doxie who is far more likely to bite than her "sister". I did check out the parks ahead of time, but I only found one that wouldn't take us because of our GSD. We decided that we didn't want to stay there anyway and found a nice park that welcomed our girls with open arms and doggy treats. Good responsible owners are almost always welcome.
We do try to pick places near things where we can take the dogs to walk, run, and play. We don't have any trouble finding places like that. One of our favorite places happens to be where we are having the OR rally in June. Winchester Bay RV has lots of grassy areas to play on, but mostly, the dogs like to walk on the beach just up the road a few hundred yards, or walk on the bike path that runs the length of the park. There are lots of sand dunes right there as long as you are careful about all the ATVs our playing on them. Those are good for you to go play!
If you can make it to our rally(info in the Events tab of the forum) that would be a good way to meet several HL people and have fun with your family and learn about your new home on wheels. Either way, enjoy your new BC and all the fun you are going to have.
Kristy