Prices for 3BRs are about 250k AED/year in Business Bay, about 300k AED/year in Downtown or about 150k AED/year in Damac Hills (far away), so I'd say 20k month is gets you a nice 3BR pretty much in every location (excluding palm and bluewater island, al barari and other ultra-lux locations). These are decent apartments. You can always rent twice as expensive in any of these locations.
Utilities should be around 4-5k AED/month (including housing, water, electricity, cooling, gas, internet/tv).
School prices average are up to about AED 30k/year per kid:
Fees (2024 Tuition) so should be AED 60k/year or for two kids or about︀ 5k/month.
That doesn't include additional costs (uniforms, transportation, excursions and other activities).
You can rent︁ a family SUV like Nissan X-Trail/Toyota RAV4/VW Tiguan for less than 3k AED/month + another︂ 500 for gas + Salik = 3.5k
So what do we have (I'll take maximum︃ amounts):
Housing = 20k/month
Utilities = 5k/month
Schools = 5k/month
Car = 3.5k/month
The total:︄ AED 33.5k/month or about $9k/month.
You would need to add health insurance, groceries, entertainment/eating out/travel︅ but as I mentioned previously $10k is doable for a family that doesn't own a︆ property.
Owning a property you would be looking at savings around 18k/month (2k would still︇ go to service charge for 3br as when renting it's paid by landlord) in that︈ case $5k/month would be a minimum.
The main thing in Dubai/UAE is to budget and︉ stick to it as you can always go higher and burn more cash. A friend︊ of my who is born and raised in UAE said to me once "In here︋ it's very difficult to save money here as you can always buy nicer car, rent︌ nicer apartment, buy nicer clothes etc". So you need to stay humble and frugal in︍ a way (and that's quite the opposite of how people see Dubai in general) and︎ you'll do just fine.