Bringing teenagers...leave tech at home or no?

First off these are not your kids so you can't tell them what to do. Their mother has to be the one on-board with the no-tech policy before you can expect them to comply. So she is the one you have to deal with.

So how does your GF feel about it? It sounds like the 2 of you might not have compatible thoughts on the subject. Resolve it between the 2 of you, and then let her deal with the kids.