I wouldn't bother trying to play the same note with left and right hands,simultaneously, it will sound just as good played by just one or the other. Without seeing the music, it's difficult to understand why you're being asked to do this - and quite unusual.for beginners, the 'cross-over ' point for each hand is often middle C, with it being played either with left thumb if it's written in the bass clef, or with right thumb if it's written in treble clef. As jjmusicnotes asked, a sample would allow us to help better. I echo the congratulations - it's never too late, but have an occasional lesson, so's you don't develop bad habits on the way. You won't regret it, with a good tutor.
This may sound strange, but you are actually trying to learn two skills simultaneously - reading music, and finding your way round the keys. They are completely separate skills, only related by the music you make. Initially, just get to know the black and white bits on the piano, and how they relate to each other, sonically, not neccessarily thinking"this is an F and this is an A, and they sound good together, " but just geographically messing about with patterns. Sorry for the protracted answer, hope it helps.