Really? The Osmonds are mormons (Members of the Church of Jesus Christ of Latter Day Saints!) and to my knowledge never dated anyone outside their faith.. I remember there was a big stink when one of the Bee Gee brothers rather fancied Marie Osmond ( I think it was the younger one who died of a heart attack suddnely) and the family were frantic. They have all married Mormons.
I adored the Carpenters and was very sad when Karen died. It was shocking. I think, if I remember correctly, that in the movie it was sort of hinted that her Mum was very critical and demanding but who really knows what the cause was. She had a short marriage which failed which I am sure did not help. Karen may have had it all, from the outside looking in, but there was something terribly sad and lonely about her!
She definitely did date Alan Osmond for a short time. He was interviewed in one of the many documentaries made about her life. Plus I have seen some home movie footage of the two of them at her parents house.
I met her a few times and she always had a sort of wise cracking, jokey, public face and a much darker and depressive private one. She seemed to be constantly worrying about things being perfect. Apparently, she got that from her Mother who also had issues - borderline OCD and a total control freak.
The Little Girl Blue book is pretty good, although a little one sided and I'm sure she wouldn't have been happy to see her Mother and Brother 'demonised' in quite the way they are in the book.
The Karen Carpenter Story TV movie is OK for what it is. It skips over/omits a lot of events and sanitises others, as it was heavily controlled by her family. They demanded many rewrites of the script. On the other hand, they allowed scene to be filmed at the family home and even had the lead actress Cynthia Gibb, wearing Karen's own clothes and even her makeup! So in some senses it has a great deal of authenticity. Worth a look if you haven't seen it.