I looked up the etymology of "father" and see what Etymology Dictionary says:
Old English fæder "he who begets a child, nearest male ancestor;"
It clearly says "fæder" with a D.
Wikitionary also has the D version:
From Middle English fader, from Old English fæder, from Proto-West Germanic *fader, from Proto-Germanic *fadēr, from Proto-Indo-European *ph₂tḗr. Doublet of ayr, faeder, padre, pater and père.
The TH was also D in middle English along with old English.
Also the word "mother":
"female parent, a woman in relation to her child," Middle English moder, from Old English modor
But the word "brother":
Old English broþor, from Proto-Germanic *brothar (source also of Old Norse broðir, Danish broder, Old Frisian brother, Dutch broeder, Old High German bruodar, German Bruder, Gothic bróþar), from PIE root *bhrater-.
I don't know what that is, but it is not D. So the change only took place in some words.
Can anyone explain what kind of change that was and what words it applied to?