I suspect getting degrees in both will be very, very hard as a practical matter. EE is an incredibly challenging major, and I can only assume technical theater major is very time-consuming with involvement in productions. (One of my kids is CompE, which is a lot of overlap with EE).
My instinct would be to be an EE major at a school where kid can work on productions, too, as an EC (which is probably many, many schools).
An example would be RIT - which actually has a big group (paid) that does some tech set-up for events: