It was intentional. To avoid offending Littlefoot. Proverbs are notoriously resilient parts of language (in fact, they can even outlive their source languages or cultures, like Latin proverbs), so it is unlikely that is there is proverb in English with a different meaning that can be applied to the same situation. The fact that you as a native speaker haven't heard of a different proverb supports this. Sometimes, a proverb can be so old that its original meaning is forgotten and it no longer makes sense, and then people attemp to re-interpret it.
You can also think of Ducky's "...or you'll fall and break your back" as her re-interpretation of the old and, to contemporary speakers of English (and to Ducky), meaningless "...or you'll break your mother's back".
And have do you know they didn't talk about his mother? The movie leaves out a lot of things. Mumbling already pointed this out ot you.
