Not a good idea to just 'mix' some cement and pour it in place unless you're pouring it about 4-6" in thickness. Doing anything less is just asking for trouble.
THe gravel will still move under/between the cement. In short order, the cement will break up. YOu need a cement base to withstand the pressures of cars and possibly heavy equipment driving over it. Yes, it's possible the gravel is too light. The best thing to do is have the 'hilly' portion of the driveway professionaly finished. I suggest steel mesh under the mix. Ask what you should do to prevent fast drying. ANd make sure there's some sort of expansion control between your driveway and the road. There, you have forces working in 2 different directions!