Yes everyone says short is better and it is true to some extent but acronyms are quite tricky business.
As a matter of fact your wife is right ..
Mgmt = Management
But a google search for Mgt shows that at some places :
Mgt is Management too
In my opinion, for Management :
Mgmt is better than Mgt but in someone else's opinion it might be exactly opposite and Mgt would be valuable because they know they can sell it.
So to avoid the confusion and hassle what I usually do and would recommend anyone is don't stuff acronyms just to shorten the length of a domain.
At NameBio, You can see domains with more than 20 letters (if they make sense) going for thousands.
And if you still want to use acronyms confirm their validity first because not every time your wife will save you from the hassle
And try to stick to valid ones like LTD, DEPT, CORP etc.