Something like this?
U1 is a CD4093 quad Schmitt NAND IC.
Pulse voltage source V2 simulates the switch.
When first pressed, an output pulse from gate U1d is generated, of duration P1 determined by time constant C1 x R2.
After a switch closure period T set by time constant R3 x C2 a second pulse is generated by U1D, of duration P2 determined by C3 x R4.
The times P1, T and P2 can be easily adjusted by varying R2, R3 and R4 respectively.
Edit: I've just realised you wanted the second pulse to start on release of the switch. I'll have a re-think ....
And can you clarify whether the switch provides a +12V level when pressed or when released?