The word piuthar is possibly the weirdest word in Gaelic for at least five different reasons. So when I wrote its plural was weird I had not even thought about why it was the way it was. But now I have.
How the s (Irish siúr, English sister changed into a p is for another day, and how the meaning changed in Irish is for the Irish course.
It appears that in Proto-Indo-European these -r words for family members had their own declension, but in Old Irish, this was replaced by copying cathair 'chair' which now has a standard plural ending in both Irish and Gaelic. So
cathair > cathraichean
So this is a standardized plural ending replacing the special ending that was once used for family members. But why does piuthar end in -ar when the other family members end in -air? In some languages they match and in others they don't:
So what we are seeing is a broad vowel in some languages, in 'sister' only, whereas other languages always have a slender final vowel. Now if we look at Old Irish, here and here we find quite a lot of confusion, but generally the nominative and dative singular have the broad vowel and the rest have the slender vowel, with the th creeping in as well. Modern Irish has simplified even further and just applies a standard plural to siúr, but Gaelic retains what is the consensus of the Old Irish forms.
My initial guess was that there there were once two words floating around in western Europe:
a word with no th and a broad vowel, so not resembling 'brother' or 'mother'.
a word with a th and a slender vowel, similar to words for 'brother' and 'mother'
However, there is no evidence that the second version existed originally, rather it seems that is is simply the word being adapted to resemble the other family members as shown in Wiktionary:
[swestēr is] remodeled based on analogy with *-tēr kinship words, from Proto-Indo-European swésōr.
So, after all that, it is quite simple. *Piur is the expected form, but the inserted th, the word peathraichean, and the English and German words all derive from an attempt to make the words sound like 'mother', 'brother' and 'father'.
Does this count as a suppletive form? I have no idea.