onewinterbaby, we skipped tummy time (gasp! I know, I'm such a rebel) because DD 2.5 yrs hated it and we found out it was for neck strength. DD was born with a curiously strong neck and I remember her standing up against me when she was 2 weeks old. Sounds like your DD is strong, too. Heck, if she's already practicing standing and walking she's holding her head up "against gravity."
http://www.devdelay.org/newsletter/articles/html/273-tummy-time-and-crawling.htmlWhat about letting her also explore some of the media around the house, like picking up puffed rice cereal, or sifting her hands through flour or a basket full of colored socks?
Also, in our case, DD wanted me almost exclusively until she was nearly 24 months old - maybe 22ish. We think she bonded completely and utterly, and then she launched. I remember her going across the street to explore the neighbor's house and holding up her hand like a traffic cop, saying, "No Mama, NO. I do this alone." She is extremely independent and confident now.
Babies are hardwired to want their Mama. It's exhausting but I hope you can wait it out and let her use you for trust building a little while longer. In my house, I took care of the baby and DH took care of me and everything else. I still felt like I was going to have a nervous breakdown, but thank goodness at least DH understood what parenting this little empress was like. None of our friends could relate to us.
Good luck, and what an extraordinary child you must have.
