I think it can be a tough thing for many men, to raise essentially another man's child. But lots of people do it, and it probably seems more daunting at first, but then people get used to it. What makes someone your child is not really the flesh and blood (genetic linkage), it's really the bonding over the years.
It does seem strange how your wife told you about one child before marriage, and the other after marriage. I'd've thought there'd be pretty much two camps. Those who would only marry a woman if she had no baggage (zero kids), and those that would marry a woman regardless of how much baggage she has (1+ kids).
Under these 'arrangements' (Young Foreign Bride-Older Western Male), I figured it'd be quite common for the guy to already have his own children, that would be pretty much all grown up by then. So when you're already coming with baggage (albeit grown up baggage), another person's baggage doesn't seem so daunting. I guess it depends on what your intentions are with your new young wife, and whether you have an interest in starting a second family (or whether she has an interest in having kids).
