Lightroom has a nice feature for this. It might look complicated but it is really easy and powerful! After getting accustomed it becomes 'piece of cake'.

1. [optional] Clear Quick Collection
2. Filter photos with the first of your kids (by clicking on apropriate keyword)
3. Select all of them (Ctrl-A or Command-A)
4. Filter photos with the second of your kids (by clicking on apropriate keyword) - important! it must be a single click change
5. Now only photos that BOTH of your kids are on will stay selected
6. [optional] If the selection alone is not enough for you - add the selection to Quick Collection by pressing "B"
7. [optional] Display Quick Collection

BTW1. You can continue to filter the third of your kids ;) and so on.

BTW2. This is a common way to find the intersection of two sets of photos. For example you can select all photos in one of your collection and then change collection to another one - now you have selected all photos that are in BOTH collection. This can be used to find the intersection between any sets filtered by keywords, collections, folders or an arbitrary selection of your choice.

UPDATE 2016-10-14: Unfortunately I have noticed important bug in LR 6 - when the intersection is an empty set LR selects a first photo!!! I guess it a new bug in version 6 that means my method is not reliable as it was.