I'm guessing since your staying at Fishing Bridge, your doing so because of the full hook ups? This means you have the opportunity to set your air conditioner accordingly and radio/TV so "Fido" doesn't feel alone.
Having had dogs my whole RV'ing life, this above is generally the way I do things. If you leave the doggies in the RV, be a good neighbor after a full day away and ask if your Pet was a bother to anyone close enough to hear a barking dog.
Just my guess, most people who stay at Fishing Bridge do so for the same reasons as you and chances are your neighbors will be out most days site seeing also. Lastly, if you do make a day of it to Old Faithful, I've always seen dogs in that area simply by staying off the boardwalks. I'm not a big fan of leaving a dog in a car no matter the weather.