some jumbled (but hopefully helpful) thoughts
Hi there ... not yet summer, so I thought I'd chime in. First of all, look online for a special TYPE of muzzle. This is one that is an inch wide arrangements of strong but thin black nylon straps that fasten with long strips of velcro. There are two circular bands made when put on - one fastens around the neck, the other around the muzzle. They are connected by a very securely stitched attachment strap that runs under the muzzle to the throat strap. Have this muzzle on ANYTIME you are outside the room.
It is often used by dog groomers when dealing with a dog that they feel (or know) might snap. They come in various sizes. The dog can still drink, even eat, with enough ease to the strap - they just can't open their mouth to bite. A dog, like an alligator, has tremendous GRIP power, but the mouth can be kept closed relatively easily.
First of all, while you can screen motels via 1-800 numbers, you may be able to get concessions by calling direct, after 8 or later at night, to talk to the night manager.
Measure your dog at shoulder height. Don't mention his possible pit heritage. (by the way, if he has shown dog aggression and wants to eat small dogs, then consider the safety of other guests and be sure to give them lots of berth and slip back inside til they are thru. You are most likely to be complained about by other guests rather than hotel employees)
If it is a possibility, you would need to know how far you would have to walk to reach a grassy area not in front of the motel/hotel (and ask if there would be an available dumpster to deposit any doggy-doo bags). Say you would want a room next to the stairwell so you would not be using the elevator. Say you would not be taking him thru the lobby during check in or check out times. Tell him how he would not be left alone in the room (well, except when you slip downstairs for the breakfast bar).
Strongly consider buying a large dog crate for him to set up in the room. It looks and sounds good to tell them the dog will have a secure crate. If you ever DO have to leave him in the room during the hours of maid service, he MUST be crated. But be aware that you can arrange with house-keeping (call them, not just the front desk) to skip your room that day - tho you will have to get any needed fresh towels later.
There are still some "mom & pop" hotels, often cheaper, often maintained by family. AND they don't have a corporate office telling them the rules. You can talk to them - maybe offer them a bit extra a night. Many of these have doors that open straight to the parking lot so you can drive your dog to a nearby grassy area for the two of you to stretch your legs if necessary. Oh yes, since he will seldom or never have a doggy park or back yard and you can't jog, invest in a 12-15 foot lead (a tie-out) so he can do as mine does, lag behind, then run ahead - and then run around me out in empty lots.
Find out about the training facility and whether they can accommodate him. If they can't/won't have him during the day, ask if they can help you find a doggy day-care facility or someone with a secure backyard. Of course, you WOULD have to bring grounding "home items" to the yard situation (toys, bed/blankie) and spend time relaxing and low-energy playing with him there - not high energy and excitement-heightening. Oh, and consider coming a day early for a yard situation. If he is an escape artist or panics when you leave, forget this one.
Lots of jumbled thoughts. Me? I snuck my dog in as I had no extra money to pay the pet premium... and then just kept a very low profile til the cab arrived early morning to take us to the airport. I was lucky as the hotel parking lot backed up on a large business park with lots of grass and it was a nice walkabout.
Keep us posted, please, on how your plans for the summer go. If everything else falls thru, consider taking your dog's pillow or blankie to sleep with and stash in a gym bag to take to your sessions. When stressed, sit down with it, close eyes, hug tightly, against your cheek, inhale deeply and concentrate on focused breathing while holding his spirit and presence firmly in mind. Kinda like meditation.
Love to a fellow pit lover ...