Your options are
A) with your 30 day visa your also given a 10 day grace period if you over stay. After that i think it's 100AED per day over stayed.
B) if you want to play it safe, you can always go to immigration, and you can have another 30 days for 500AED each.
Or
C) take your family on a day trip to DOH/BAH somewhere cheap on flydubai, be careful tho as you've got to pay on entry to get into Qatar so sometimes it's not worth the hassle. (don't know if this has changed since I last went)
Hope this helps.