I'm a second "wife" (not married but only for tax reasons) and have two stepsons aged 12 and 9 and a daughter with my partner of 2.6.
I think there are myriad pitfalls to second families, not least financial issues. But resenting the first family is a surefire way to unhappiness.
I don't agree with Xenia that you should avoid having a second family though, in order to avoid financial hardship. Our daughter is the making of our second family (we went through a lot of pain until she came on the scene) and I know lots of second families who say the same - the stepsister/brother reconciles the children from the first family to the final ending of their parents' relationship and creates a shared bond of joy between all of us. I don't love my stepsons in the way I love my daughter, and they don't love me the way the way they love their parents, and that is normal and right and I wouldn't want it any other way, but we all unite in a common love of my daughter.
What's more, it makes me a better stepmother (which I would have been in any case) to have a child of my own, more tolerant of children's foibles and individuality.
But basically we all get on very well anyway. I'm very lucky.