I too have Playskool fingers - I swear at times they look like Ballpark Franks and I had a heck of a time fingering chords without stomping all over the neighboring strings. Like has already been said, in many chords, that's actually a good thing. But when they get in the way when they're not supposed to, I find it's because I don't have my thumb positioned right and I'm attacking the strings at an angle rather than straight on. For me, keeping the thumb on the lower(bottom third of the back of the neck with the tip of the thumb pointed skyward) edge seems to allow me greater range and feel with my fretting fingers.

And great tip about tilting the neck back and forth to get a peek. I do that now. But I will say, it does get better. Like your analogy on typing, after a while, you just kind of learn where the strings and frets are without looking. It's actually really sort of exciting when your fingers go right where they should and you don't even think about it.

And major kudos to you for playing along with your daughter for encouragment. Not a lot of Dad's would do that.

Good luck. :)