With your 31' and towing a car - if you're traveling in the West you will have no issues using public parks such as national parks, national forest campgrounds, COE, state parks, county and city parks. Definitely no problem if using RV parks.
We used all the above with our 40' motorhome towing a car - no trailer. Parking the car and the trailer might give you problems however many parks have a separate area where you could park the trailer while there.
Are you talking a trailer or a tow dolly? Those with a dolly seem to have it easier because they can sometimes tuck the dolly under the RV without needing a lot of extra space.
The eastern public parks might be a problem except for some of the spacious sites in the COE parks. RV parks shouldn't be a problem in the east.
Personally, I wouldn't worry about it. There are always places nearby to where you want to stay that you will fit. It'll just take some research by you. Enjoy yourselves.