Assuming all 4 bodies are in coplanar orbits. Best case:
Planet A is furthest from star B at the time of ejection, planet B furthest from star A at the time of insertion. In this situation the spacecraft needs to escape from planet A's orbit, raise the apoapsis to intersect the planet B's position at the predicted time of insertion, coast, and do the insertion. If both planets orbit their respective stars in the same direction the apoapsis will need to 'reach' behind star B, if they orbit in opposite directions the apoapsis will only need to reach the planet in front of star B (difference of 2 orbital radii of planet B).*
If we fit two Suns into roles of the stars and two Earths as planets A and B, each orbiting their respective star at 1 AU with stars themselves being 25 AU apart and we both launch from and end up with circular R=7M orbits, we get:
3.13 km/s for planet A orbit ejection
11.57 km/s for transfer orbit insertion
11.57 km/s for star B orbit circularization
3.13 km/s for planet B orbit insertion
total: 29.4 km/s
If planet B orbits in the opposite direction the situation changes dramatically:
3.13 km/s for planet A orbit ejection
9.93 km/s for transfer orbit insertion
roughly 50 km/s for star B orbit circularization (at this point star B accelerated you to around 40 km/s towards it)
3.13 km/s for planet B orbit insertion
total: over 65 km/s*
The delta-v is so immense because instead of using the star to do the heavy lifting (by capturing at periapsis) it's all done by the spacecraft. I think.
Movement of each star in its counterpart's rotating coordinate system was neglected (~10 km/s), and the integration was approximate to say the very least. But it should give a rough picture of the dv requirements for that flight.
Double sunset over Tatooine comes to mind
* I know this kind of a trajectory is idiotic, halfway through the calculation I realized that by doing a retrograde capture (flying an "8" transfer instead of an elliptic one) the dv requirements would be close, if not identical, to the previous ones.