Sir this is not big deal, what you have to do, you can go to immigration office and meet with captain and request him for family visa extension. They have authority to extend up to 2 month but mostly they do only for one moth.
Second thing if you send your family back then there is no restriction or ban you can apply again visit visa and bring your family again to Qatar.

Here is complete process to convert visit visa to RP

http://www.qatarliving.com/visas-permits/posts/process-convert-family-vi...