Disagree.

While you have not been here long enough to experience the need to change accom (yet), there will be a time in the near future when your current accom comes up for renewal. When the accom department refuses to pay beyond the current limit (120,000 dhs), you'll be asked to:

a) pay for the extra out of your own pocket to stay where you are, or
b) move to cheaper accom that will be chosen for you.

Should you decide not to uproot the family and stay in your current home you'll feel the direct impact of the cost of rents in Dubai on your bottom line. It's coming.