Need budget replacement for broken kit lens - am I missing something?

Just a thought, have you looked back at your photos from before the lens broke and after, looked at the percentage of wide and telephoto shots and what you really feel you are missing without being able to use the D60.

I have a 35 1.8, love the lens but it would not be my go to lens when taking photos of my teen daughter when she's with her friends.

Indoors with a few friends around, candid, it's probably not wide enough unless you have large rooms.  If your daughters play or start sports or similar activities then outdoors it's likely to be too short. In other words it could be as limiting and frustrating as your p&s or phone cam. On the other hand if you find you did your pre-breakage photos around 30-40mm then a prime could be ideal.