Seems like there are lots of good advice in this thread and some, in my opinion, not so good advice.
First of all, I own the Tamron 18-270 VC, the first version, not the PZD. This is the lens that I've owned for the longest time out of all my lenses (and many more that came and went in the meantime).
I also owned every Rebel at one point in time from the xt (350D) to currently owning the T3i.
I used the T2i a lot with the Tamron 18-270 and I liked it a lot, while keeping in mind its limitations. I also own some expensive lenses but that fact does not take away from my enjoyment of the Tamron. I am originally from Hungary and I've taken my Tamron lens - with 2-3 different bodies at different occasions - to Hungary many times since 2008.
The T2i is one of the best entry level DSLR out there still to this day in my opinion. IQ is very good, virtually the same as 60D, 7D, T3i, T4i. So that shouldn't be a problem. Feature-wise it is also pretty good and should not limit you in most of the shooting situation you might face.
The lens is a good all-around lens, I love it for traveling light/vacation. Some advice. Unless you're in a low-light environment, or want a shallower depth of field for portraits, stop the lens down by 1 stop at any given zoom setting (e.g. use perhaps f/5.6 at 18-35mm shots, use f/8 at 200+mm shots, etc.) That helps achieve sharper images AS LONG AS you're not compromising shutter speed and causing motion blur. The VC in this lens is great, but it won't help freezing motion by your subject (kids, pets running around, cars, traffic, etc.)
And this takes me to the main advice other have already given you: getting a basic understanding of photography. There are a tons of good books out there, also on the internet. But perhaps the most beneficial is to find a friend, a colleague, who knows about these things and can explain them to you in an easier language. Yes, technical terms are important to know but friends have a better way to explaining to us what they mean and do.
So to sum it up, your 550D + Tamron 18-270 VC is a good all around combo if using the right skills and knowing its limitations. And no, there is a good chance that you will not be able to take top notch wedding photos, portraits (here I mean images that look like the ones from professionals who own state of the art lenses, full frame bodies, the necessary skills, etc.), or award winning bird photos etc. There are way more specialized and more expensive lenses for that. I myself don't just venture out with my T3i and Tamron lens to catch migrating warblers in the area. I use my other setup (7D and 120-300 2.8 OS with extenders) for that purpose.
But don't give up, your Canon 550D is a very good body and the Tamron lens should provide you with a lot of nice memories.
p.s. I also believe that you should not lose the superzoom. I, in fact, went from starting out with the Canon 18-55 IS + 55-250 IS combo which I liked, to the Tamron 18-270 VC. For walk around, vacation photos, to me, the Tamron fits the bill better. With the 2 lens Canon combo I occasionally missed shots due to not having the right lens on, I found myself changing lenses all the time. I also faced more dust and dirt getting into my camera when I was on the beach in Tampa and had to change lenses to accommodate the shooting situation.
So I think you're fine with the superzoom.
Now it's time to hit the books, the net and ask friends about advice.

One last advice. I think your next steps equipment-wise should be an external flash, even if it is the cheaper 270EX, and the Canon 50mm 1.8. That will expand your indoor and shallow depth of field (for portraits for instance) possibilities.
Agreed. An external flash and the Canon 50mm f1.8 should be on her short list for future purchases.





