Better yet, cancel the whole thing. I'm sure businesses thought this might have been a good idea, once, but it's clear it hasn't worked out that way. Unfortunately this has probably become an "entitlement" to too many, and some judge will think so too. So they're probably stuck with it.
They can't. They can't stop people of a particular race from coming to a particular place on particular dates.
They can enforce nuisance-abatement laws - public drunkenness, nudity, noise, no-turn-signal, and so on. Occupancy guidelines for lodging could be enforced. Businesses should be allowed to close at will.
Apart from that, one runs afoul of free speech and free association rights. I think a motel should be allowed to say, "I won't rent to a black person during this time period," but that's not within the current understanding of civil rights.