1. Is "on est là avec [quelqu'un]" an usual way to express "[someone] and I are here for you" ?

It is indeed a possible way to express Moi et papa, on est là, i.e. "you can count on us".

2. Would it be unusual to say "moi et papa sommes là/ici pour toi" ?

That would be formal (because of the lack of subject pronoun and the first person plural tense usage) and unexpected in a conversation.

1. Is "on est là avec [quelqu'un]" an usual way to express "[someone] and I are here for you" ?

It is indeed a possible way to express Papa et moi, on est là implying "you can count on us".

2. Would it be unusual to say "moi et papa sommes là/ici pour toi" ?

That would be formal (because of the lack of subject pronoun and the first person plural tense usage), slightly less polite than papa et moi as Greg commented, and unexpected in this conversation, especially as on was used instead nous.

In a very formal family (or in the 19th century book), that conversation might have read:

Mère, renoncez à la boisson. Papa et moi, nous sommes à vos côtés.