As far as I am aware, clann refers specifically to children and not to a broader family. See here or here for examples. That being said obviously páistí obviously also means children. Perhaps others can give one or the other more validity.

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Thank you so much again Cúmhaí!

Would the correct word to use be clann or chlainne ?

Clann is the word in its basic form. "Chlainne" is a specific mutated version due to a grammatical context, and is the correct one for this example.

An excellent explanation. Thank you Gumbi!!

So here are the final choices that I'd love spelling/grammar confirmation on and then I can leave you wonderful people in peace!

ar son mo pháistí OR ar son mo chlainne ("For the sake of my children")

mo pháistí - mo chuspóir OR mo chlainne - mo chuspóir (my children – my purpose)

mo pháistí - m’inspioráid OR mo chlainne - m’inspioráid (my children – my inspiration)

No it should be "mo chlann" or "ar son mo chlainne". The rest are correct.

Just to be particularly clear, here are the correct grammatical forms as said above by Gumbi:
ar son mo pháistí / ar son mo chlainne
mo pháistí - mo chuspóir / mo chlann - mo chuspóir
mo pháistí - m’inspioráid / mo chlann - m’inspioráid

Before you proceed with them, I would look for final confirmation from a heavily experienced or native speaker that these are idiomatic. There are a thousand ways to put together a phrase that would have a similar meaning, but hard to know what would sound normal or what would sound strange to an Irish(wo)man. For all we know an alternative like mo pháistí - mo bhrí could be the obvious best choice and it didn't even cross our minds. Is fearr glas ná amhras!

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Thanks again Cúmhaí. That is what I had figured after a few reads

I dearly hope I can get a couple more confirmations as it is so important to me, and I need it to be as close to 100% correct as humanly possible!

Again, I am so grateful for all the assistance I have been given so far!

Hi,

Sorry to rehash my post, but I have thought of another way I might like the same sentiment expressed, and was hoping someone could please advise how to say "They are my reason/purpose"

Thank you so much yet again!