Intense white oval shape seen in cumulus cloud after rain storm.

My son and I were driving on highway 695 when I saw an intense, white oval shape hovering in a big white cumulus cloud.  It hovered in one area for a couple of seconds, then darted to the left, then the right horizontally.  Then it went straight up and then down after which it repeated the same pattern a couple more times in and out of this cloud.   I had not said anything to my son at this point because I wasn’t sure what I had seen.  After this display, my son says to me, "Did you see that thing in the sky mom?  Stop the car."
I pulled over to the shoulder and took out my phone and started recording the objects motions.  After a couple of minutes it darted into the cloud, came back out then went back in and never returned.  We sat there for a couple of minutes waiting for it to reappear but it never did come back.  Once it disappeared my son noticed a fighter jet circling the same cloud we were looking at, as if it were looking for what we had seen in the cloud.  
Another plane then proceeded to follow around the cloud cover as if it were looking also.  This went on for another minute or so then they left.  We were not far from a military base at the time.  We have several in area.