No...this is how it should go down preferably.
If you need the DP to come out on the first possible frame, You do the DP+P then hold the P, while it's held, start your motion for RDP, that gives you an extra 4-5 frames to do it. Once the first hit of the DP connects (hell, maybe SLIGHTLY before it), hit and hold K.
It just requires practice, it sounds harder than it is. The main thing is just getting down the motion from going from DP to RDP.