These posts she is putting up can in future be deleted and how do you know her FB isn't private?
This has to one of the more ignorant posts I've read this week. Nothing you post on the internet is deleted. It does not go away. It may disappear from your screen, but it is there and stored forever. There are servers dedicated to just copying what you have posted in the internet and storing it. You can never access or delete that content. The EU has passed laws (right to be forgotten) and Google will not delete content. They will only conceal it.
Secondly, anything you post on FB is their property. Their copyright. You have no right to tell them what they can and cannot do with information you give them. If they choose to use your baby's picture to advertise their site, sell your kids photo to The Sun after it's hit by a truck, or publish sisters photo is FB's Worst Dressed, you have no recourse.
Lastly, just because YOU can't access someone's FB account, and they selected the tick box, 'private', does not mean the vast majority of the computer literate world does not have access to a FB page. It's not like they have state of the art encryption or anything.
So post your kids photos online, and list their birthdays and their places of birth. I'm sure they won't be dumb enough to use their real DoB or place of birth when they open a bank account, and I'm sure DD, if you have one, whont be dumb enough to use your real Maiden name if you have one.
Play liberal with their personal information, but at the very least, teach them to lie about their place of birth, date of birth and mothers maiden name in future life. Otherwise you're just compromising their future security.
Computers never forget anything. In 20 years if someone wanted to know about Michael Andrew Jones from Wakefield, everything his parents published online about him will be on a database somewhere. All you'd need to do is know how to look.
Posts I made in 1992 are still available online. The sites no longer exist. Entire internet companies hosting those sites no longer exist. Yet they are still there, archived on computers around the world.
It will not be long before people start complaining that they cannot get a job because of stuff they posted online. Prospective employees may well be profiled (filtered) online the same way we filter out the incompetents and the wannabes with CVs today. Do you really want to adding to that information source without knowing how that information will be interpreted, or what it will be used for?