Ask her to join you in making a big deal out of turning off your phone and putting it away when spending quality family time together. Explain to wife that it's just something you read about raising girls these days and once they become teenagers getting them to separate from their phones is near impossible UNLESS it's been family habit/tradition for years.
Act like you didn't even talk about this concept the other day because you don't want to be telling her this phone idea of yours like you are explaining why your wife was ridiculous to be mad the other day when she tried to make it out like you were merely trying to punish her. Let her draw her own conclusion that EVERYTHING isn't all about her all on her own.
THEN...maybe..a small part of her will miss EVERYTHING you do NOT being all about her.
Great job inviting her. I think she'll come. She'll tell herself it's good for your daughter to see you two getting along and co-parenting. She hates missing out on these moments.
The internet is 90% complaining and entitlement and I hate it because I deserve better!