Additionally, it's commonly known as habitual "would" and it's near synonymous with
used to. I'm not all that convinced it goes well with "so Mum decided to punish them." More context might sway me, though.
Correction #1
EX: The children would make
a lot of noise, . . . .
"a lot" sounds like one word, but it's actually two; It's written as two separate words. Test: a
whole lot. You can put a word between "a" and "lot".
Correction #2
Mum and Dad are capitalized when used in place of the person's name. For example,
EX:
Mum/Jane likes cake.
EX: . . . so
Mum/Jane decided to punish them.
But note,
EX: My
mum likes cake. (no capital; correct)
EX: *
My Mum/My Jane likes cake. (capital; incorrect)
"My mum" doesn't replace a name. "Mum" does.
All the best.