Hello everyone!
I was looking to get a tattoo in honor of my grandmother from Cork. Her mantra was always "Strength in Family," which she roughly translated it to "Neart i teaghlaigh."

Because it is for a tattoo, I was wondering if her translation was indeed correct.

I have also seen this translated into "neart i dteaghlach", or with capitals: "Neart i dTeaghlach" If anyone could please help me out that would be great! Thank you.

The word teaghlaigh is the plural form, so these two are (literally) correct for what you want:
neart i dteaghlach
Neart i dTeaghlach

However, when moving from one language to another, it is sometimes the case that the definite article ("the") would be used in one language where it would not be in the other. I think in this case it would sound better to say:
neart sa teaghlach
Neart sa Teaghlach
which would literally mean "strength in the family", but wait to see what others think.

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

I'm wondering if "i" is the preposition that would be used here. It works in English, but my inclination would be to use "trí" (through) in Irish. Maybe that's just my ear playing me up, though.

Redwolf

That's a good point, Red, so maybe:

neart tríd an teaghlach
Neart tríd an Teaghlach
"strength through [by means of] the family"

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

Yeah, tells you more of the origin of the strength using the tré/trí

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__̴ı̴̴̡̡̡ ̡͌l̡̡̡ ̡͌l̡*̡̡ ̴̡ı̴̴̡ ̡̡͡|̲̲̲͡͡͡ ̲▫̲͡ ̲̲̲͡͡π̲̲͡͡ ̲̲͡▫̲̲͡͡ ̲|̡̡̡ ̡ ̴̡ı̴̡̡ ̡͌l̡̡̡̡.___

Maybe you could also translate it as
Strength from the family
Neart den/as an teaghlach

but I don't know that if "the" is totally necessary.
Maybe someone with better Irish can clarify, I never really know when you use the article and when not....