Like WP02 said, it's 100% in the hands of the regional host through the championship. The only exception is if the host region had previously decided during their regional meetings, that the championship game would be played on X day and/or at X location. (If anyone knows of a Region that has in-fact, made such a declaration, please let us know). This is the autonomy that the the member VHSL schools are granted and basically insist upon.
Having said this, "usually" the two competing schools will work together to accomadate one another. As eluded to above, it's not unheard of for a host school to use a date or time to "hinder" or "annoy", a school.
The Golden Rule of the VHSL is that the Regions are to provide a regional champion on the established date for the semi-final games. How they come up with a regional champion is totally and 100% up to the region.
The state semi finals and finals are governed by the VHSL, not the member schools or the participating schools. These are THEIR games, (VHSL). Currently, they dictate that each State Semi-Final game will be held at the facility of the two competing teams that had the higher VHSL Power Points total at the conclusion of the REGULAR season. (Your playoff seeding is illrelevant. An eight seed in Region A could conceivably host the 1 seed from Region B.) And each Semi-Final contest will be held on a Saturday. There is however, a process, formal and informal, that allows the VHSL to listen to consideration of changes of venue, date and time, during times of extrodinary circumstances.
It's a darn good system gals and guys.
Perfect? No, of course not. But neither are any of the alternative ideas.