Bella is Absolutely the Adoptive daughter of Carlisle and Esme and the Adoptive Sister of Jasper, Alice, Emmett and Rosalie. The text backs this up.
1. Parallels with Emmett
She Entered the Family in the same way that Emmett did but he is always accepted as the son/brother not the "son in law/brother in law". He married into the family and was transformed by Carlisle and from that point on was considered a son the same happens to Bella only she had been considered a daughter before hand. If one considers Bella the Daughter in law/Sister in law then they would have to consider Emmett to be a son/brother in law instead because he has the exact same entrance as Bella just much quicker. Also Emmett's parents would have been
2. Use of Daughter/Sister in the Books versus the non use of in law
Bella is never called daughter in law/sister in law ever, she how ever is referred to as daughter/sister in every reference to her by a family member. Carlisle refers to her as his beloved daughter in book two of new moon, Alice in book one, and Emmett always does "not much wild about you is there little sister" "i haven't gotten to dance with my new sister yet" "you're going down little sister". Not once is she called the "in-law". She also openly calls Alice her sister and means it not in an in law way but in the way someone refers to their real sister. She is also always treated as the daughter not as the sons wife.
3. The difference between a vampire family and a traditional family
The vampire family unit is different from the normal family. Intermarriage being the biggest part, everyone of the six siblings has the same four brothers and sisters as their mate and the same parents it's slightly disturbing in the margot and ritchie tennenbaum sense. However it is less formal then the conventional family it is easier to more like a foster family which it pretends to be. The biggest way in which they are connected is their vampirism and their vegetarian philosophy.
4. The Fact that Charlie and Renee are alive means little
A person doesn't need to have dead parents to be adopted thats an orphan. The fact that Bella retains some of her relation to Charlie also is irrelevant many adopted people are in contact with their real parents. the fact that she continues to be connected to Charlie is just Stephanie Meyer's inability to leave any character with a sad ending a flaw that Jane Austen and early Charlotte Bronte also had. One can have two sets of parents and Bella does. Emmett and Rosalie's families were still alive though they had the sense to remain dead to the public Alice's were not remembered and jasper's would have been long dead
5. Adoption v. joining the family
Bella joined the family gradually not at the wedding and since it wasn't a typical or legal adoption it was more of her becoming their daughter just as the other five did. These reasons are why Bella's page needs to read that she is the Cullen's daughter/sister it's what the text says and what Stephanie Meyer is giving us. If you can make a better argument i'll go your way but if you can see it my way that would be awesome as i strongly believe it and need to be proven wrong as this is a Democratic medium and debate is the only way.