Well, it's not really that you hate her kids, right? You don't actually know them personally. And what you see on FB etc. isn't reality--people don't post their bad, ugly moments, so their lives might look perfect, but chances are they're not.

From what you write it seems like this is much more about your own insecurities, and about standards that you imagine your T has to which you don't measure up. So maybe you could talk to her in general about that, what about FB gives you the idea that you're not meeting some criteria for a good or worthwhile person, what those criteria are and where they come from. And while I kinda think maybe you should tell her you looked up her kids, you could easily just talk about how FB etc. affect you in general without mentioning that specifically.