When you do meet the children keep out of her relationships with her children. Withhold your opinions (insights, guidance, discipline) if she is not parenting as you think necessary. No matter how much she asks for your input, or how much the children appear to need or love you, if you get prematurely entangled you will ultimately come out second best.
You are at your most helpful when you support, empower, encourage the woman to tap into her internal resources to be fully the mother she is able to be. She has to do this without you if she is ever to be comfortable sharing this with you.
Withhold your opinions about her ex-husband, visitations, her finances, how he treats her or how he treats his children. This potential minefield predates you and you will be better off as a couple if you regard it as none of your business. A relationship built on trying to correct the injustices of her past will not bode well for your future.
Your distinctness (separatness) is more important than your necessary ability to bond with the woman and her children. When the time comes and bonding with both mother and children is necessary, your distinctness will be a life-saving necessity both in the immediate and in the long-term future.