I'm no great mechanic (though tend to be pretty fearless), nor am I particularly amazing with a soldering iron (though I'm not awful).
I actually used to make a living soldering and unsoldering components in a past life.
I thought I would chime in with a few tips.
Of course good tools make for good results. A temperature controlled soldering iron is the best, most don't have one, but if you play around with stuff it is a useful tool. Doesn't need to be adjustable
An 1/8 wide or so chisel tip is good for this job. Pointy doesn't get enough heat, super wide too much.
There are big etches on the board, they suck up a lot of heat, so be patient.
Add some flux core solder it will help get the heat into the joint.
Solder suckers work better than braid[solder wick]. Even the tiny turkey basters work ok
I have one of these:
desolder all the pins to that they appear clean, they will probably still be stuck
using the iron tip push the pins back and forth. If you get it just right you will get just enough heat to break the last solder bond. If you overheat it it will remelt
Now grab the relay body and try to wiggle it, flip it over and touch the iron to break the stragglers free.
This is a single sided board, so the risks are really low, it is kinda hard to mess up with fat etches and none on the other side.
If dealing with a double sided board sometimes it is better to cut the component apart before desoldering rather than risk pulling an etch up off the top of the board.
Pull the etch off of a 5 layer board[IOW it has a layer of etch in the middle of the board, in addition to one on top and bottom] and see the look on your bosses face!
seems like this kit:
and some relays and you would own the tool and be cash positive compared to buying a new CDL module.
Seems like the relays they use in all the modules are suspect, so this might be a useful skill to learn.
Just about the only things that die in modern electronics are electrolytic caps[the can looking ones] and relays.