goldenroses95, you are right, she is wrong, and I wish you all the very best in the world in keeping her unpleasantness at bay.
This "babies ought to be fed every x hours" thing (when I had mine, in the eighties, it was every four hours rather than three, and we were very strongly encouraged to bottle-feed and made to feel like bad mothers if we breast-fed) was from the advice of a man called Truby King.
Truby King lived 1 April 1858 – 10 February 1938.
He also advised not cuddling babies in case they grew up to be namby-pamby (not his words, but that was what he meant). And if they cried you should ignore them, for the same reason.
He probably meant well....
Nobody mentioned cluster feeding to me when I had my son in 1981, in fact I'm not sure it was really known about, but my son knew about it, and made sure that I found out pretty damn quickly! For the first four weeks of his life he only stopped eating to have his nappy changed and take short sleeps before he started to cry for food again. He's a six foot two marathon runner now, so it doesn't seem to have done him too much harm.
My mother-in-law didn't approve, but luckily she lived 150 miles away so we didn't have to see her too much.