RP or tourist visa?

Hi everyone, I'm new in QL. been reading for months.

I wanna ask bout family residence permit for me and my son. I've been here for 6 months on family visit visa under my husband sponsorship. My visa will be end at 30 January. We already bought tickets fly back to our home country at 20 January, as we thought my husband's contract will not extended. But surprisingly, a month before we back, the company extends his contract until April. We've tried to ask bout my visa to his agency who handles this matter. At first, he said it's okay for me to go home and back to qatar with a new visa. Then, just few days ago, he told us, I couldn't. Even more he said it takes 2 months to finish RP process which made me decided not to count on him again and we will process it by our self. Then the problem appeared when we found that we need to fulfill all the requirements and hand them to Immigration department immediately. We rushed to Gharafa immigration today to ask is it possible to finish all the RP process for less than 2 weeks. They said "maybe"

does anyone experienced the same case? I mean, you can finish all the process and get your RP for 2 weeks or so? or can I can go back here on tourist visa (but not under my husban sponsorship) ?