Yea that looks pretty messed up. I guess first I would want a purpose of the circuit. Is it to allow the digital pot to control a 0-5 volt output source?.
"Am I wrong in choosing a transistor for this job?"
Yea, I think so. You would probably have better luck not having the transistors at all and going from the pot directly to the adjust pin on the regulator, but you would have to check up on a application note somewhere on how to control the regulator externally rather then the normal feedback resistor. Transistors are current amplifiers, not direct voltage amplifiers, so they have to be used in circuits using bias and load resistors to generate a voltage output.
What else could I use? I can't use the MCP4251 itself, because its pot terminals aren't rated for more than +/-0.3V of VDD.
Again it's not clear what the overall objective of the circuit is. What result range are you wishing for at the DVM terminals, and how much current capacity do you wish for? The key specification missing is the full voltage range you are looking for from the regulator circuit. With regulators like this there is problems getting lower then around 1.2vdc and your pot has a 5vdc input limit. So the complexity revolves around the range you want, as below 1.2 and above 5volts will require a non-simple circuit.
Thanks for looking :/.
no problem
PS: Yes, I'm using the LM317 correctly, I just don't know why I can't get the transistors to work like I want.
Again if the transistors were working as you want, what would be the result?
Possibly doing some research on available documents, you might find a circuit example that could apply:
http://www.national.com/mpf/LM/LM317.html#Documents
Lefty