Sounds like your in "a rock and a hard place" sitation.
If invites were sent and only her name on - then she really should have checked about hubby and kids but it seems alot of people assume that 1=all.
Personally , I would always check.
Would love to know how the party goes. Hope her kids behave in a reasonable fashion. You shouldnt have to police your house, but I wouldn't hesitate in reminding her to watch her own children. You cant be expected to keep an eye on them all as the host, each parent should be watching their own kids- thats fair. Perhaps even explain some basic house rules to the kids when they get there?