H2 isn't massive, but as noted previously, tire width may be questionable. Try emailing them the question. All car washes I've been to disclaim any liability for potential damage. There's a hand wash place on route 130 north bound in no Brunswick that I've used that have done a good job for me, that would not impose any size limitations.
If the wheels are stock you should be fine. Fold it your mirrors and remove the antenna if you can. Is your Hummer lifted?
I've never had a problem but I have a sedan with no extras on the outside. The only thing I see is because of the width of your tires you may not be able to use it.
I wouldn't recommend it. If it will mess up anything on the outside of it. They will not be responsible for any damages that done to it.
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