Need words or expression that get the meaning right without resorting to using simple ones like "shouting" . I'm trying to describe a house with kids where a lot of activity is happening
Words like racket and din could lead you to other synonyms. Lexico has
1 A loud unpleasant noise; a din.
the kids were making a racket
Another suggestion is, from Lexico
1 A chaotic din caused by a crowd of people.
1.1 busy, noisy situation.
You could say
Our house is always a hubbub of activity.
Cacophony (Noun): A harsh discordant mixture of sounds.
"a cacophony of deafening alarm bells" Lexico
The word ruckus can be used. Google gives the following definition and provides an example with a child:
a disturbance or commotion.
"a child is raising a ruckus in class"
Clamour (Noun): A loud and confused noise, especially that of people shouting.
Example: From behind the group, a great clamour arose — Lexico
It can also be used as a verb.
Tumult (noun): A loud, confused noise, especially one caused by a large mass of people — Lexico
Example: a tumult of shouting and screaming broke out.
It's a bit more dramatic, but "pandemonium" (Noun) comes to mind.
"Wild and noisy disorder or confusion; uproar." Lexico
I would go with bedlam —
a place, scene, or state of uproar and confusion
There was bedlam in the streets after the verdict was announced.
Example usage, related to a house full of people, from the UK paper The Guardian
My wife and I live here with our five kids, our grandson and three dogs. I run my executive recruiting company from here and my wife runs a childminding business in the conservatory. It can be bedlam sometimes.
I like bustling. As in "Sorry about the noise, our house is bustling with activity this morning." From the OED:
That bustles (in various senses of bustle v.1); esp. (of a person) that moves about in an energetic, noisy, or busy manner; (of a place) full of bustle or noisy activity.
Shemozzle is what I used to call my chaotic household of 6 kids.
"A state of chaos and confusion; a muddle." Lexico
Boisterous means "loud, clamorous, and unrestrained." Think of children on a playground or a lively party or a litter of puppies as boisterous. This word, which comes from Middle English, can also refer to very intense storms. You could call a hurricane boisterous, but you will most likely hear this word used to describe people.
Tintinnabulation (Edgar A. Poe--"The Bells")
Although it certainly does not have the direct connotation of "children" and the garboil that they may cause (p.s. "Garboil" although an archaic word may itself work in this context--and it sounds just so wonderful too!), the word (tintinnabulation) certainly evokes a sense of "madness," and if the reader realizes the allusion to the word and to Poe's poem, that may in itself become quite a virtue, as then you paint into the reader's mind that spasming, tempestuous atmosphere that Poe so brilliantly portrays--therefore relating Poe's madness to a flock of children screaming about:
"From the bells, bells, bells, bells, Bells, bells, bells—" (Poe)
A classic phrase to describe the sounds of a house with young children is to describe the pitter-patter of little feet. Literally, it describes the gentle sounds of young children who are just learning to walk, and has a joyous connotation of a home full of life. One could use the phrase sarcastically, or twist it to the pitter-patter of big feet or the clomping of little feet, to describe a house with not-so-little children who are running around and making too much noise.