Have you opened up a dual shock controller?
From what I remember there is not much room inside them and the board is quite a precision fit, you won't be able to get much in there is you are not using surface mount devices.
I am not sure sure what you mean by an emulator chip to use PS2 to vertex adaptor instructions. I presume you are talking about some form of microcontroller, if so and you are going to change existing code or write your own from scratch?
If you are modifying existing code that is proven to work using the same microcontroller then you should be off to a good start so why not program it so that it can convert the dual shock to outputs for Coleco, Vectrex, 5200 and game port then you just have one adaptor board for multiple systems.
If you are writing your own code from scratch you will probably find that much harder, particularly as there are two versions of the dual shock (A & H in the serial number) and one is much fussier with the timing of the clock/data on the SPI bus than the other, on the lower clock rate of the digital mode you will probably be ok but at he higher clock rates of the analogue and advanced analogue modes you may find that only one type will work with your adaptor. Consequently it may be simpler to convert to output of the dual shock to Vectrex adaptor where all the hard work has been done for you to be compatible with the Coleco, 5200 & game port.
I presume you are talking about the old style PC game port with the 15 pin D connectors as modern PC game controllers are USB, if so will the analogue output be the same type as the game port input? In the game port the analogue stick acts like a variable resistor (connections to wiper and one end only) that varies the current available to charge a capacitor with charge time being relative to position. If that in the Vectrex controller is acting like a potentiometer it will be outputting a voltage instead which is not compatible.