I don't know if my story completely aligns with yours tracey but I will use it here to show other strange things that proves you are not nuts or that we all are.
I am sure everyone has heard of the idea of singing to the child while still in the tummy and sticking with one or two songs so that it soothes them later when they are born. We did that ... for some reason I was messing with one of my dogs and started singing 'In the jungle' replacing The Lion with the dogs name. And The baby with DD name. The first time she was fussy I started singing that song and she stopped crying instantly to listen to it. Very sweet indeed. She now sings the song on her own (of course our revised version)just out of the blue it is either that one or Puff the Magic Dragon.
None of that is the weird thing ... when I was pregnant with her I would fall asleep in the crash and burn type. One night or very early morning I woke up to my DH tapping on my belly. I almost made a comment when I felt DD tapping back the same beat to him. I was stunned and figured it was a fluke so I stayed still and he did it again but changed up the beat and she repeated it back. I was freaking out at that point and sat up and made a comment about did you feel that she is mimicking you. He just laughed and said yes, she has been for weeks. We have been playing a lot while you are asleep.
To this day she has amazing rhythm.