Abba_S your points are good ones, and I agree that bad relationships with the kids and ex can be a deal breaker or ruin a second marriage, and Lavender needs to know what she is getting in to. And finances must be discussed.
But considering that they have not even discussed his divorce and kids, it is too early to bring the kids into the picture or ask to meet them. When it is serious, she will meet them. I do not think it healthy for kids to be meeting every girl their father dates, only the one who will become their step-mother, and it seems that Lavender is not yet at that point.
even if all goes well, and they do reach the point when she meets the kids, I am not sure how much she will be able to tell by meeting them- as you say, dynamics will change as the kids get older, and even when they realize what it really means for their father to be married to someone not their mother, and have other kids with her who will get more of their father’s attention than they do… it is hard to predict how people, especially children will react. And the dynamics with his ex also may change if she is jealous that he is remarried, and she not, etc.
Better than how the kids or ex-wife responds, I think is how the father responds- when conflict arises between kids and new wife, whose side will he take? Will he be truly supportive of his new wife and her struggles to accept his kids and deal with his ex? Will she feel like the outsider when the kids are visiting, or will he present a united front of “we are the parents now” to his kids? How will he deal when the kids challenge his new wife’s authority?
I think these are important things to work out with him while dating, neither of them can predict or control how the kids or ex will behave, but they can work out how they will act and react to these situations, and that is ultimately what is important. Even if the kids or ex turns their lives into a living nightmare, if the father is truly supportive of his new wife and they can build a strong marriage, they can survive the nightmare.