This looks useful
https://archive.org/details/historyofnorthum06nort/page/72/
Long article. Says Agnes was Hugh's grandmother.
We're told that Bernard II left no kids, or siblings even, and his English estates were inherited by his French cousin Eustace, who came to England and remarried.
There's massive internet confusion over the wives of Eustace.
Hodgson says the second wife was the widow of Robert fitz Piers, citing the Pipe Roll for 2 Ric I (1190-91), which I can't see online. Which tells us very little.
But Eustace's heir Hugh was in arms in 1201, so clearly the son of the first wife. I'd imagine she was French and Hugh was raised in France.
I’m moving over the children of Eustace de Baliol to Ada de Fontaines
It seems unlikely that Perronell ‘Petronella’ could have been their mother, chronologically.
The profiles affected:
Hugh de Balliol, of Bywell & Barnard Castle
Source: https://fmg.ac/Projects/MedLands/SCOTLAND.htm#EustaceBalliolMAgnes