Is there any rule and reg that regulates the number of miles you can require an employee to commute to an event outside of a normal work day without compensating hotel stay?

there is no such reg...sorry. As far as a rule, common sense applies. If I'm closer than 100 miles, I'd just as soon get home. Of course, depending how late I'll be at the function also dictates whether I'll stay over...

I couldn't find anything that gave a specific answer, but if you check out

http://www.irs.gov/publications/p17/ch26.html#d0e60134

it vaguely mentions guidelines for hotel stay considerations.