Wow. 7 people of those ages in one 30' TT! All traveling in one vehicle? I think you are only allowed one vehicle plus the trailer.
May be hard to conceal for a whole week. But, I think if it were me I would just go ahead with the plans. Just be very discrete coming and going during the day. And never have more than 4-5 people outside at any one time. And be very quiet when you are outside. And have a backup plan if they ask you to leave. West Yellowstone is not too far away and has a number of RV parks that you might be able to get in to if you are asked to leave. But they may also have that or a lesser limit.
