Dude. You can do this. Just heat up the end of the diode that needs to be soldered for a bit, then touch some solder to it (not to the iron) and let it flow onto it. After coating it a little bit, do the same thing to the hole with the red wire coming through it. With a little bit of fresh solder priming both sides it will be super easy to solder them together. Then put the two parts together and heat them up together until the solder flows. You could even bend the broken diode's lead (wire) slightly and touch it to the lead of the diode next to it, and solder it together that way if it's easier.
I can't even imagine what the problem could be. What kind of iron are you using? Is it melting the solder easily?