D.B.
Yes, you're doing it wrong. You seem to think that the purpose of having children is to get them to show that they love you every second. You even want to have a second child to see if you get one who shows love to you more? Please, please do not have a child to give it a "job" to take care of you!
She's 2. She's normal. She likes to see people other than the one she sees the most. You probably are pushing way too hard, and you may be driving her away with your insistence on closeness as you define it. Stop trying so hard, back off, and give this child a little bit of space. She will be handicapped forever if she is smothered by you. She's enjoying a little bit of independence to make her own choices (for a 2 year old, that's who she's going to run to).
And children don't have an automatic affection because of a biological connection, so saying "she's not our child" is really very damaging and cruel. Adopted children are loved just as much as biological children are.
This is either a phase she's going through (most likely) or due to your insistence that she pay attention to you (which is backwards - it's up to the parent to be the caretaker). Stop expecting her to act like a much older person and meet your needs. Please get a book on childhood development by talking to your pediatrician or a good children's librarian so you can learn more about normal behaviors in children of varying ages. If this doesn't help, please see a counselor to help you straighten out these very negative thoughts.