I’m in need of some help with a translation from English to Latin. I’m in the middle of designing a tattoo and the client wants the sentence ‘A moment in my arms, a lifetime in my heart’ to be written in Latin and has sent over the sentence ‘momento in arma mea vita, meum cor’ but has used Google Translate to swap the English to Latin (and we all know how Google Translate likes to butcher translations). I would greatly appreciate any help on the matter.
You're quite right not to trust Google Translate! The sentence it gave you is nonsense.
A "moment" in Latin is either a punctum or a momentum; out of the two, I like punctum better. (Punctum comes from the word for pricking something with a pin, while momentum comes from a word for movement and motion, if that affects anything.) It's often found in the slightly longer phrase punctum temporis "moment of time", but in context it could be understood without that.
A "lifetime", as in a long span of time, would be a saeculum rather than a vita. (A vita is literally a "life", but it's more like a biography or a living soul than a span of time.) This can mean literally a human lifetime, or figuratively a generation, or figuratively a hundred years (which the Romans considered something like the maximum possible lifetime).
One standard word for "arms" is bracchia; Vergil and Ovid use this word when talking about embraces, so it seems good for your purpose. And "heart" is straightforwardly cor, both literally and metaphorically.
Putting it all together, with appropriate endings on the words: punctum in bracchiis [meis], saeculum in corde [meo]. You can swap in momentum if you like it better without changing the overall meaning. The meis and meo literally mean "my", but can be left off here where the context makes the meaning clear; leaving them off makes it a bit shorter and cleaner.