Problem in FSK demodulation
Well, if you can stabilize the PLL a bit more this is going to provide better pay-back when it comes to recovering the data but, in the absense of any improvement, you could try passing the signal through a high pass filter that has a cut-off close to the data rate frequency.

It should remove the lower frequency up-and-down wobble (to a large extent) but will tend to turn your data into edges like this: -



And, to recover the "differentiated data you could use a comparator with significant hysteresis or use two thresholds (either side of 0 volts) that set and reset a flip-flop. You could even low pass filter the data signal to make a signal that tends to follow the undulations (coming by the PLL) and use this to modify the thresholds to counter any undulations remaining after high pass filtering.

I've had to do pretty much that same on one job I was involved with and was very happy with the results. The amount of undulation superimposed on the signal was very similar to your example but, I would certainly start by trying to improve the PLL because any gains in removing the unwanted undulation makes life easier on the detect (data slicer) circuit.

Following on from the edit in the question I have a couple of observations about the PLL parameters: -


I think that your VCO quiescent frequency should be about 3 MHz and not 1 Hz
Given that the PLL output is up to 10 volts I think the VCO sensitivity is OK at 1 MHz per volt providing you make the centre (quiescent) frequency as I suggested. 



  What I have observed here is that as the data rate changes, the
  property of the PLL filter output changes and which makes me to
  readjust the PLL for every significant change in this sample time


When your data rate slows down and heads towards the low-pass frequency of the PLL loop filter you might get problems that are dependent on your application. Some applications allow the PLL VCO to track the modulated frequency (a fast loop filter) whilst other designs will want to keep the VCO at roughly half way between the two FSK frequencies (slow loop filter). It's unclear as to what your design is.