Okay so I'm pretty new to being openly poly however I do think I've got a great deal of experience with relationships in general and having a poly mindset so I'll give responding to your post a try.
Firstly there's no reason you should feel obligated to enter into a relationship with your SO's other partner simply because you both have a relationship with him. For you to have a functioning relationship with her, you would have to be interested in her as you are your SO. As you both have him in common it's likely you'll have shared interests and such but it doesn't automatically mean you two will be interested in each other anymore than civil aquaintences. You have to determine for yourself if you have attraction to her and not be pressured by the situation to enter into that.
Determining whether you and the other girl need a degree of specialness from your male partner is something that you each need to determine on your own. Some relationships could function where much is shared between all partners but as individuals we all desire some degree of independent identity and things that are uniquely "ours". This varies from person to person and what you might desire would be different than someone else. It would be best to communicate these desires to all parties involved to make sure everyone's needs are met.
Her establishing that she's been given everything you've been given could be reflecting insecurities she has on her end in an effort to stake some sort of primary claim to the relationship. Having a frank discussion with her and the guy about how this makes you feel might be a good opening for her to open up dialogue about how she's feeling as well and you will be able to establish boundaries that work for everyone.
Hope this helps!