The problem is that if you couldn't solder that as it were, it is doubtful you will be able to solder the repair of how it is now.
I cannot see your pics very well, there is too little color and bad lighting. However from what I "think" I see, the top switch pin just gets soldered to the copper all around it, just take a knife blade and scratch away some to expose bare copper.
The middle pin, follow the trace to the next point it connects to on the circuit board. You can then take a piece of solid core wire, something like network cabling wire (around 24AWG), solder the switch front pin in, make sure the switch is tight against the board and loop the end of the piece of wire around the middle switch pin, pushed tightly against the circuit board then soldered.
Next solder the other end of the wire to that "next point" above. If you can't get the switch to remain motionless doing this, you might have to give up on an "easy" repair next time and epoxy the switch to the PCB with a bead of epoxy on both sides, or super glue or whatever, making sure none gets into the switch. Epoxy being thicker than super glue will be easier to work with, IMO, won't creep into seams in switch housings as easily.
Really what I would do in your situation, if this mouse has value to you and you need use of it soon, is find a friend who is good at soldering and ask them to fix this. It is better to practice your soldering on worthless scrap parts before putting it to task on something of value. Also consider that it is much harder to solder with a bad quality iron and/or one with a shot tip, especially until you get good at soldering and realize when the tip is unusable or just needs cleaned.
A little plastic bodied switch like that, will be damaged if heated too high or too long during soldering.
