Welcome to the forum. Can you give us a little more information? Seems like if it shimmies only under braking I would look at out-of-round front rotors. Easy enough to check, just pull the front tires and spin the rotors. If they are binding or tight in certain places then it's your rotors. While you're in there check for play in the ball joints and tie rods.
It could be steering/suspension (ball joints, tie rod ends, etc) but it's hard to tell you from your description.
Time to pull a tire and look, or take it to your favortie mechanic.
Also, tire balance can be an issue at those speeds.
You may already know this but your motorhome is on a Chevy P30 Chassis. Pretty easy to get parts and advice for these common platforms.
1986 Airstream 345 Classic Motorhome