MA mi familia y yoa mí nos preocupa porque solo tiene dos años, yo lo compré la semana pasada.

Algo (sujeto) te preocupa a ti (objeto indirecto).
No sé por qué incluyes en esta frase hace cuánto lo compraste. A nivel semántico queda raro.

MA mi familia y yoa mí nos preocupa porque solo tiene dos años, yo lo compré la semana pasada.

Algo (sujeto) te preocupa a ti (objeto indirecto).
No sé por qué incluyes en esta frase hace cuánto lo compraste. A nivel semántico queda raro.

It is a detail that for me personally alludes to my family and I not knowing the dog that well and exemplifies the worry/concern of the writer

Does a mi add emphasis ?

If that's your aim, I would try to connect the sentence to the rest of the text. It feels weird because you just leave it there hanging. My recommendation would be adding it to the previous sentence: "A mi familia y a mí nos preocupa porque solo tiene dos años y lo compré la semana pasada.". This would make sense because you said it should exemplify the concern.

Well, I would say it depends on how you interpret the sentence. You could, in fact, remove the tonic complement and it would still make sense: "Nos preocupa porque solo tiene dos años [...]". You can add it for two reasons: First, it could be a matter of emphasis (like you said) or, second, it could be to explain who that first person plural includes. Bear in mind that you hadn't mentioned your family until now, so it makes sense to explain who that "nos" is to the reader. If your question is about the possible omission of "a mi" and just writing "A mi familia nos preocupa [...]", this is sometimes done in colloquial speech. I personally don't recommend it because it is grammaticaly counter-intuitive and can result confusing when hearing it.

Mi familia y yo nestamos preocupados porque solo tiene dos años, yo lo compré la semana pasada.

Llevo más de dos días que buscaándo por élo.

Llevo más de dos días que buscaándo por élo.