How did Dick endanger Holly's children?

It may not have endangered the children physically, but it definitely endangered their well-being because it greatly increased the chances that they would have ended up orphaned that night.

I don't think that Hans would have sent someone after the children, but because it gave him the knowledge that Holly was someone important to John, it enabled him to use her as leverage against him.

He endangered her children in multiple ways:

1. sending his TV cronies and who knows who else to the kids' house that night, when only the housekeeper was there to protect them

2. giving Hans valuable information and thereby endangering Holly and John, the kids' parents

3. putting the kids' faces on TV at an extremely vulnerable moment

4. exposing the kids' identities to Hans and/or his allies for possible future retribution

While Roger's answer sounds reasonable enough, I think that there is a possibility that Holly is referring to some event between the two movies and unknown to us.

There are several hints throughout the movie that there was a lot of media fuss around John after the events at Nakatomi Plaza. It is not that far-fetched that Thornburg, an unscrupulous and fame-greedy reporter, went beyond simply paparazzing John and Holly.

And if we take a look at the hit from the ending of Die Hard, Holly punched Thornburg's nose (well, it's clear that Bonnie Bedelia actually missed William Atherton, but her hand is in the height of his nose), and not his mouth (to take out two of his teeth):

And he's holding his nose, not spitting teeth:

As John and Holly enter the limo, Thornburg also asks the cameraman "Did you get that?", clearly and with no blood going out of his mouth (or nose, for that matter, meaning that the punch was not that hard).

I don't think that this was ever thought through by the writers or the directors of either movie. It's just a small comedy element, but since this question is here, I t think that this is a possible explanation.