For native french speaker it does not sound ambiguous.

Actually many of native french speaker use “on” instead of “nous” which is not true correct french.

Quand on était gosses, on nous taquinait beaucoup à ce sujet.
means “When we were kids, we were being teased a lot about this topic”

And therefor should be translated :
Quand **nous** étions gosses, **on** nous taquinait beaucoup à ce sujet.

Originally the french “on” is more like the english “it” while not totally equivalent.

This dual use of on with different topic is very common. Nevertheless if you would like to speak proper french you should use “Nous” when appropriate.

The second ‘on’ here doesn’t refer to “someone/they”.

I believe it is what is called “un pronom impersonnel”, in the same way that “il pleut” does not refer to anyone: it is used when the action has no specific actor.

Regardless, as a native french speaker, this sentence is not ambiguous at all.

It doesn’t sound ambiguous at all to me and it’s exactly the way I would say it.

And on nous taquinait (we were teased) cannot mean on se taquinait (we teased each other).