Learn English – the document called that parents have to sign so their underage children can take part in something

You could ask "Are you the oldest child?" (or even "eldest child"). This seems to me to be more natural. Note the use of "the" before the adjective, which you omitted.

Pedants would note that "oldest" implies at least three children. If you know that there are only two children, then you could ask whether the colleague is the older child.

A slang expression for parents who behave in such a way is Helicopter Parents To quote the Oxford Dictionary definition.

A parent who takes an overprotective or excessive interest in the life of their child or children

As has been suggested it is worth noting this is quite a recent inclusion into usage.