You can live a decent life on it but what about savings? Remember there is no safety net here - if your husband's employer decides that he doesn't have a job anymore then its a plane ticket home (and sometimes the need to repay housing advances and education benefits). You can stay and look for another job but no guarantee one can be found quickly. There is also limited pension provision (there's end of service benefit but no true pension) and you need to save to make sure you have coverage for that. How much you want to save is a personal decision (and based in part on your current financial position) but remember to deduct that from the amount you have left over.
Also remember to deduct the cost of vacations from the amount you have left over. Even if it's just one trip home a year using the employer flights. If you need to hire a car, rent accommodation, meet up with/entertain friends and family that one trip back over the summer gets expensive quickly and does need to be budgeted for (I'd say at least 2k a month). That assumes you don't want to travel on top of that.
A comment on kids activities - this is where I feel that the UAE is often unexpectedly expensive. I spend about 4k a month on kids activities for two teens (and I'm not including their socializing cost). You can spend less of course, and kids can do less, but depending on the activity be aware that it may cost more than you're expecting.
On your specific numbers:
Rent - I'm not up to date on latest Abu Dhabi housing prices (I am in Dubai now) but 200k seems low for a 4-bed. Are you sure that is achievable in an area that is a reasonable commute for work and school?
Education - You are allowing 62k per child for school fees (based on the fees allowance and the addition 3k per month). Depends on ages of children and the schools you're looking at, but have you found schools at that price point that have availability? Remember that school fees increase as children get older (and salaries don't always).
Utilities - 2.5k is also low (as an average) for utilities for a 4 bed in my experience unless it's a new and energy efficient 4 bed (in which case rent of 200k seems v unlikely) - remember you pay 5% tax on rent as part of utilities so that's 800 alone before you start paying water and electricity.
Maid costs - You may also be underbudgeting for maid costs - on top of salary , you need to account for visa, medical, food, flights and annual bonuses. That comes to about 2k on average a month (front loaded because of the visa costs) and then whatever you pay for salary (which depends a lot on what you're looking for - mainly someone to clean/do laundry, someone to be more of a housekeeper, or someone who will have significant childcare obligations). Unless you're working and need the childcare, a maid is a nice to have of course but once you've employed someone it becomes a commitment (and visa costs are frontloaded anyway).
Transport - Agree 4k is low for transport, unless you have the capital to buy cars up front. You may be able to cope with one car if your husband taxis to and from work, but that will be a taxi bill of around 2k a month (depending on distance of course).
Phones - Do the kids have phones? Decent internet will cost about 500 a month, then the mobile phone packages will be 200++ depending on calls/data.