I had a slide pin shear off and we had to use heat to release the slide pin from the hole, remove the calliper from the car to reduce the risk of fire. I don't know what tools you have or your abilities but you could buy the torch and a heavy duty vice grips or get a local private garage or car engineering firm to remove it. Get replacement pins and boots ordered and remove the rubber boots from both pins there will be a lot of heat and the torch needs to be powerful to keep the heat on the spot as it will soak away into the rest of the calliper.
forgot to mention it looks like someone has tried to drill into it in the past...
Might be looking at a new caliper?
Not sure how far that hole goes and what is at the other end, but could shoving a punch down there and giving it a whack maybe loosen it up?
I'm fairly limited with the tools I have and I really need to get the car moving again today. I can probably just about fit the caliper back on with new pads/disc. If I leave that pin stuck could it cause major damage to anything until I have the time to get it fixed?