I recently bought a Williams Black Knight whose batteries leaked, and unfortunately the blue fuzz dropped onto the driver board underneath onto a few components, one of which was the flipper relay. Somehow the corrosion got inside and I can see it damaged the parts inside the plastic cover. The other affected transistors on the board were easily removed and replaced.

The rest of the board is good, I just need to remove the relay and solder in a good one, but I cannot seem to desolder this one completely enough to remove it. The lugs are almost as wide as the through holes and seem to allow just a little solder to remain between the two, even where it looks like it was all removed under a magnifiying glass. I'm using a Hakko desoldering gun with a 1.5 mm tip, what should I be doing differently to get this damn thing removed?

Tried everything I could think of last night. Added new solder and tried again. Tried solder wick and flux too. And all the lugs/tabs seem to be sticking straight through. I don't know what else to try; maybe leaving the tip in place a little longer to heat it up more, but I don't want to risk lifting the traces. Are these single-sided traces or through holes?

Yeah, that's probably what I'll have to wind up doing. I was hoping this thing would come out easier, as I have another junk driver board and was hoping to desolder and reuse the relay from that, but the "scorched earth" method of removal kinda precludes that.

Follow-up question: when I bought the game, the upper right flipper coil was already burned. Could the damaged flipper relay have been the cause?

No propane torch handy so I took @cheddar's advice and cut it off piece by piece with a dremel. I must have done a fairly decent job of desoldering in the first place, as 13 of the 14 lugs were able to be extricated by hand, though they were tight. That tightness and the one that I still had to desolder meant that cutting it off was a necessity.

Pics of the corrosion inside the relay below, and a few step-by-steps. New relay awaiting installation. Hope I never have to do this again.

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I have seen those sockets. I've never had or seen another bad relay, this one just happened to be located under a leaky battery. Probably/hopefully something I'll never have to do again, but I have spare relays now.

I got that. I have another driver board that may or may not be working that I was going to harvest the relay from, but I figured, why destroy what may be a working board for one part if I can source a new one elsewhere?