we just decided one day to take our lifting a bit more serious and progress on squats
nothing beats that feeling of training with a strong girl who can keep up 
!
any advices or comments you guys have on our form and that method ?
I wrote a reply and somehow deleted it, but here are the first things I noticed:
1.) Shoes; get some solid shoes for lifting! Flat sole for powerlifting, weightlifting shoes for Olympic lifting / Crossfit / etc.
2.) The girl (sorry not to use her name; you didn’t give it) needs to work on her depth and form before progressing to daily max-ing, and it probably wouldn’t hurt for you to do the same. I suggest you spend a month or two (at least) working with lighter weights and plenty of assistance work - Sam Byrd’s CAT 5x5 setup is ideal, though I’d suggest doing it twice a week for squat rather than once, and having two separate front squat days for triples. From there, progress to hitting 85-95% daily over another month, then jump into the daily max + back-off routine when you are okay with that (it’s not going to be easy, but should become routine and not stressful mentally - at least, until you add back-offs!)
3.) The best of luck to both of you; high frequency, high intensity training is tough but can be extremely rewarding for many lifters. Remember to be strict with your technique, especially maintaining tension in the core, EVERY SINGLE TIME YOU LIFT. This is vital for safety / injury prevention and simply lifting heavy weights!