Ive done several connector replacements to date and they have all gone very smoothly using a soldering pen. But i wouldn't say you have to replace the connector altogether, if you think your connector is faulty for whatever reason try rejoining the posts to the pads first, this will establish whether your solder joints are bad or if for whatever reason your connector is "faulty" in another way.
But if your still looking at completely replacing the connector....
As long as you have a fine tip soldering pen and possibly a hot knife tip you should be able to get the connector free. You'll also need flux, extra solder, qtips and isopropyl alcohol. The only part of the removal process that will be kinda unconventional will be getting the two mounting points at the back of the connector free. The two mounts will require to you remove the plastic around them,I melted the plastic, then you can unsolder them. These points are structural to the connector and do not provide a connection from the battery to the board. The four pads on the other hand need to be dealt with in a very careful manner. Ive used very thin solder braid to pick up the solder around the base of the pads. Then with the pen I applied heat to each pad and "wiggled" it free. Keep in mind that there are several very small resistors near the pads, DO NOT damage these!
After you free the connector from the board do some house keeping, prep the pads with fresh solder, clean off the board with alcohol and make sure the surface will let the new connector sit properly. If you can manage all that, getting a new connector back in will be easy. To make sure the connector is going to stay put, use a dab of supper glue on the bottom of the connector and place it on the board lining the posts up with the pads. After the glue dries simply resolder the pads to the posts on the battery.
I cant give you much info on how to use a reflow gun with this because ive never used one to replace this particular part. But if I was going to do it off the top of my head I recommend making a heat shield that will cover everything but the connector. Tinfoil works best in this case since you will have to cover corners and bends. Make sure you add flux to the area youll be applying heat to. As far as the temperature, I would use about 700 degrees ferinheight. And remember your not going to hold the nozzle directly on that area for very long, 1-2 seconds at a time, keep that heat rotating so you dont burn your board!
Unfortunately i cannot really explain the finer points of soldering, it really is an acquired skill working with liquid metal.