I want to get “family” incorporated into a tattoo but, knowing there are multiple associated words, want to ensure that I use the appropriate word. As a believer that blood makes relatives but loyalty makes family, I want the term that best encompasses chosen family but does not exclude blood family.

"Family" is a very frequently asked question though not so easily answered.
You could read the answers already given.

But unfortunately, the search function of this forum doesn’t want to search for "family" alone, so I put in "family" & "teaghlach" - a common word for family (though rather meaning "members of household"):
search.php?keywords=family+teaghlach&terms=any&author=&sc=1&sf=all&sk=t&sd=d&sr=posts&st=0&ch=300&t=0&submit=Search

There are dictionaries with helpful explanations for every word online:
https://www.teanglann.ie/en/eid/family (de Bhaldraithe, English-Irish)
https://www.teanglann.ie/en/fgb/family (Ó Dónaill, Irish-English)
https://www.focloir.ie/en/dictionary/ei/family (Ó Mianáin, English-Irish)

I’d prob. use muintir, or rather "mo mhuintir" (my family/folks).

Mo mhuintir

People have different opinions, and it can vary by location, but muintir [mo mhuintir when you add the word "my"] seems best for what you intend. Traditionally, it can refer to your wider family, and even include your "people" (those from your home village or area), so it can have a broader sense than teaghlach.

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

Thank you for everyone's input.
I will be getting "Mo Mhuintir" when I set up an appointment. I appreciate you all taking the time!