You will want to be in the Nordelta area for the kids or one of the surrounding suburbs because most of the English speaking schools are in that area. It won't be too convenient for you if you have to work in Puerto Madero so you will have commute time but you're going to be limited with wanting a 4 bedroom house. You can easily find a 4 bedroom house in Nordelta or surrounding area. Very safe area. A house like you want will probably cost between $2,000 to $2,500 dollars per month at a minimum.
For tuition figure at least $500 dollars to $900 dollars per month per kid depending on which school they go to. On top of the rent you will be expenses to pay HOA fees for the gated community. That will be around $300 dollars per month. I assume you will have a car or 2? Cars are expensive in Buenos Aires. On top of the cost to buy the car you have to have insurance which will be about $100 to $150 dollars per month per car.
Health insurance depends on which plan you have but for a family of 5 on a good plan you will probably pay at least $1,500 dollars per month.
Utilities on your house will be around $300 dollars per month including electricity, gas, water, internet/cable.
And most people have maids to help them clean. I assume if you're working unless your husband wants to clean that would be another $200 to $500 dollars per month depending on how often they are coming.
So that is about $5,500 dollars not accounting for anything else. Dining out can really add up as restaurants aren't as cheap as they were before. Forgot what your friends said about mid 2023 as prices are much higher than that now. Prices are at least 2.5x what they were then. Some 3x.
With a family of 5 you will spend a significant amount dining out to eat and groceries. I would budget whatever you are spending where you live now. Food here isn't too cheap besides a few items. Many things are more. Beef is much less than back home. Chicken pork too but some things more.
Your budget will depend on quality of life you are accustomed to back home. With a family of 5 I would say calculate about $7,500 to $8,000 dollars per month to have a good life here.
Remember that inflation is slowing down but prices are still going up. We have about 3% per month inflation here. I made the move here but my wife is from here. We have 2 kids that were born here. I am not sure I would recommend making the move here with 3 young kids especially right now.