What‘s the meaning/correct translation of „athbhaile“ into english?

It's the term usually used for a second home.

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I'm not a native (or entirely fluent) speaker, so be sure to wait for confirmations/corrections, especially for tattoos.

Thanks Caomhin!

Are there any more opinions/agreements in that?

Also, if I may add, you could say "holiday home" or a place where you spend a lot of time.

Thanks!

Would it also be a translation for „home from home“? Or is it more a translation for a residential second home like a second house i.e. in a different country?

Ó Dónaill gives:

athbhaile, m. (gs. ~, pl. -lte). Second home; home from home.

So, yes, it means "a home away from home".

ár n-athbhaile "our home away from home"

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WARNING: Intermediate speaker - await further opinions, corrections and adjustments before acting on my advice.
My "specialty" is Connemara Irish, particularly Cois Fhairrge dialect.
Is fearr Gaeilge ḃriste ná Béarla cliste, cinnte, aċ i ḃfad níos fearr aríst í Gaeilge ḃinn ḃeo na nGaeltaċtaí.
Gaeilge Chonnacht (GC), go háraid Gaeilge Chois Fhairrge (GCF), agus Gaeilge an Chaighdeáin Oifigiúil (CO).

Thanks a mill guys.

And how would you actually pronounce „athbhaile“?

Athbhaile
AH-WUL-ih
/a:ˌwa(:)l´ə/

Like abhaile (see following), but with a long stressed A at the beginning:

https://www.teanglann.ie/en/fuaim/abhaile

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WARNING: Intermediate speaker - await further opinions, corrections and adjustments before acting on my advice.
My "specialty" is Connemara Irish, particularly Cois Fhairrge dialect.
Is fearr Gaeilge ḃriste ná Béarla cliste, cinnte, aċ i ḃfad níos fearr aríst í Gaeilge ḃinn ḃeo na nGaeltaċtaí.
Gaeilge Chonnacht (GC), go háraid Gaeilge Chois Fhairrge (GCF), agus Gaeilge an Chaighdeáin Oifigiúil (CO).