Could this be read as mini-wife behavior?

I am in a unique situation as my girlfriend's daughter is less than 10 years younger than I am (she's 16 and I'm 24). She also has a more confident and outgoing demeanor than myself, as I am a textbook introvert who is also rather shy and soft spoken in nature.
Because I am not expected to discipline her or play any kind of "parental" role, I am often left wondering what on earth my place is in her life besides her mother's younger, same-sex significant other. (Note: my SO and I have been together for almost 4 years, and I met the kids two-and-a-half years ago).

Before I begin, I feel I have to make a disclaimer: I'm not sure whether I am just viewing this from a jealous lens or whether there is an actual motive here, so I need some of you stepmoms to help me analyze what is going on...

Anyway, since I have gotten to know her, I have noticed that SO's daughter seems to believe that she knows what is best for SO and will often tell her what she needs to buy and where, etc. Two or three months ago, the three of us were in Wallgreens together and her daughter (who was practically ignoring me) walked through the store next to SO looking at the sunscreen, going on about why SO should buy one particular brand as opposed to another based on the price, etc. In fact, she went so far as to get down on her knees and compare the ingredients. After that, she went on to something else and said: "Oh, mom, WE NEED".....It was as if I didn't exist to SO's daughter, and even if I did, I sure wasn't in a position to tell SO what we need and what we should and shouldn't purchase. Although I didn't say anything to anyone (to either her or SO), I began to feel my blood boil underneath my skin and rolled my eyes behind her back (so neither of them would catch me in a state of extreme irritation).

Fast-forward: SO's daughter notices that there is little food in the refrigerator, so she says: "WE need to go grocery shopping, mom" (and, by "we", I am assuming that she means she and SO, as opposed to the THREE of us..The reason I think this is because she hardly ever addresses me when I am with her mother. She will always say "hi, mom", or "bye, mom", even though she knows that I am in the room as well, and this has been the case for a long time, even though she is otherwise courteous to me and isn't blatantly mean or disrespectful in any way).

Fast-word THAT: SO texts her daughter mentioning later on that she is not feeling well, to which her daughter responds: "Awwww, yeah, you should get some rest"....Is it just me or does this seem like something a daughter wouldn't necessarily say? I didn't find it outrageous, but I did find it a bit odd--it was as if her daughter was taking on the role of the caretaker, which I feel is, and should be, my role in her mother's life.

Fast-forward THAT: SO and I recently had to purchase a new car. SO's daughter's boyfriend recently bought a new car of his OWN, which he found on ebay, and SO's daughter was advising SO to look on ebay herself and BUY a new car as opposed to leasing one. She has to give her a list of all the reasons why SO should buy a car and was rather relentless about it. Fortunately (kudos to SO), she didn't take her daughter's words to heart and we went along and leased a car ANYWAY. However, after we purchased a great car for lease, she had to text SO asking about all the details of the car, including whether it was bought or leased, etc, etc. SO looked at me, read me the text that her daughter sent, and asked how she should respond, as we BOTH felt that what she was asking was really none of her business over all and were getting a bit personal (she knew we bought the car together and SO mentioned that I paid for it).

I'm too afraid to mention this to SO as SO already knows I am jealous of their relationship and will more than likely narrow it down to that, dismissing my "petty" concerns. I know a lot of stepmoms on here deal with, or have previously dealt with, mini-wife behaviors in stepdaughters. Should this be a cause for concern or am I just being jealous and/or paranoid?