As a parent of two boys I see this the opposite way. I see restaurants and driving as good times to interact with my children (with them nailed in place) and also for them to learn how to entertain themselves and to learn appropriate behaviour. As far as I'm concerned the use of technology as a general pacifier is much more of a problem than anything else - I'd quite like my children to have some kind of attention span before technology inevitably takes it away.
I'm not suggesting we're luddites or saints though - my kids still watch too much TV and play too much Minecraft but I think of them as entertainment devices and not off switches for children.
As another poster suggested - your vows will be like so much dust in the wind once you have a real kid running about, forming its own personality (e.g. talking back / having tantrums) so I believe you just have to do your best to hold on to (a little bit) of your core beliefs, be flexible and let kids be kids. And don't listen to strangers with advice.
All the best with the little one.