Take heart! If your research leaves you with more questions than answers, that just means you're doing it right - after all, every ancestor found means two more to look for! ;)
But to get to your real issue, we just need to take a careful look at this:
First of all, with the 272cM, can we verify that we're not missing a decimal point? Below 30cM, they tell you to the tenths of cM, so "27.2cM" would be a possibility. It doesn't really sound like that's it, because you call your relative a "Second Cousin", when you clearly are unsure how you're related. I presume you mean she's listed under Ancestry's "2ND COUSIN" list. That doesn't necessarily mean that she really is a 2nd cousin, but the 272cM would have to be correct to be in that category.
So, assuming 272cM is right, I can tell you that the Shared cM Project Chart WORKS, although 90% of the values I have in my own matches are a little lower that the averages given (and I wonder if the ranges are a bit too wide sometimes). Also, I'd point out that it's just as important - with a number as high as 272 - to notice what relations it CAN'T be, as it is to see what it CAN be. What I'm saying here is that it's basically impossible for 272cM to be a 3rd cousin or more distant.
So it looks like you're really fairly closely related, but with the 272cM being so high above the table's 233cM number, I have to wonder a little if there isn't something slightly special going on here - by which I mean endogamy. In other words, you may have more than one pair of common ancestors.
It sounds like you have at least two great-grandparents in common. If you have enough relatives who have done the test, and put in enough data so you can tell how they're related, you ought to be able to used the Shared Matches feature to see which two great-grandparents they are.
Good luck!