>.would electronic be better than in-person when you're in the cave?

Answering from my own experience, electronic is better. It's an IRQ (interrupt request) and can be prioritized to just after the current Intractable Problem folds over into the Inevitable Solution, which a great time for a break.

A personal visit is an NMI (nonmaskable interrupt), on the other hand, can't be prioritized or postponed, and often smashes the stack badly enough that the Inevitable Solution can't be reached again directly, only through painful reverse-approximation ("Nope, that fragment wasn't it.") The same applies to the telephone, should you be so unfortunate as to have one in your cave; at least mine has SIT tones at the beginning of the outgoing message, which throws off autodialers.

Unfortunately, doing something like hooking up a doorbell switch at the entry to the BratCave to an unused serial port's status line will allow absolutely anyone (the kids included) to generate multiple spurious IRQs. Maybe installing a cardreader terminal intead, handing out magstripe cards, and restricting their access times...