Re: relay control module joints look ok...
It is the temperature of the pin/terminal that determines the strength of the joint. The solder will melt very quickly and the thin layer of copper on the PC board will get hot from the molten solder, but the terminal will take a little more heat.
I think it is best to wick away the existing solder and carefully clean the terminal as it will have corroded where it was not covered with solder. They may not have been clean enough to start with.
With the terminals cleaned use a resin cored solder-not acid cored solder or acid flux- and a nice hot soldering iron. The six joints mentioned in the original thread are the ends of bus bars and are not liable to be damaged from a little extra heat. Use a nice sized soldering iron resting a good area of the the iron against the pin, or the heat applied to the terminal will be carried away faster than you can get enough heat to it and prevent it getting up to the soldering temperature. This may have been the reason they fail.
Solder comes in a variety of alloys, you do not want to use the type you use on your copper plumbing for instance. Using acid flux will give you more headaches down the line. It is acid and eats away at the metal until it is spent or totally removed, OK on big copper pipes but not dainty terminals.