My own advice on de-soldering would be:
1) Apply new solder to the pins to be desoldered first
2) Clamp the board in a vertical position
3) Place nozzle of desolder tool over pin - touching one side of the leg
4) Squeeze trigger and hold for a second or two moving the nozzle around the leg to ensure all the solder is removed.
5) Repeat from 3 for all pins involved.
6) Hold board up to light, if you can see light through both sides try wiggling the pin with your finger.
7) If persistent, clamp board vertical, apply heat with soldering iron on leg on other side of board while desoldering on solder side with tool.
duratool de-soldering rigs are not the best in the world but they will do the job - keep the nozzle cleared using a reaming tool and keep the tip clean.
Theoretically the chip should either press out from the reverse side or be easily wiggled out with a pair of angle nosed pliers - don't exert much force doing it this way as you can lift traces easily on some boards.
Get a second hand Metcal SP440 or Hakko and change all the filters on it and you'll have a better experience.
If you get a really persistent pin - take a break and let the board cool, then apply lots of solder to that pin and then desolder - it should clear out.
I went through this trouble, I generally can remove all IC's without snipping pins so I can test them out of circuit.