Why do mum's always say: 'Put your shoes and socks on.' to the little ones, instead of: 'Put your socks and shoes on' ?

Perhaps because shoes might be worn without socks, making socks a secondary accessory.
Like I might say "I was wearing Mary Janes with white frilly socks and my boyfriend was barefoot".

This reminds me of this totally impromptu, unscripted scene from "All In The Family." The producers liked it so much, they decided to leave it in the episode.

[media=https://youtu.be/prRtcQz8Uqk]

Yes, come to think of it, it is a strange way round! One we hear so often we tend not to notice the word-order and pick up only the message.

not if you've had enough to drink

don't ask

Dads say it too.