You really do not understand what we're going to do. First of all, most of her extended family is expected to surrender and we probably won't execute the whole lot, only those we know did things that are actually execution worthy. If we did that sort of thing it'd hurt us politically more than it gains us, see the way we treated the Essosi.
Second, if she works for us she can get new power, a new institution and even a new birthright for those children (I want to give Castamere to that Reyne guy we found, but there'll be empty castles galore around Westeros so I'm sure we'll find something for her).
Third, she has children. That means no crazy gambles and no guerrilla war campaigns, because you can't take children on those and she has nowhere to stash them.
Fourth, you're misreading Lanna. She's not that concerned about holding on to all she has, nor does she despise us. Refusing to target Daenerys because she's a little girl is not the action of someone who is willing to do anything in order to keep her position.
Finally, she just can't do what you're worried she might because you can't pull two parties worth (seriously, we've a shit-ton of Companions) of high level PCs and gear out of thin air.