^^ Does your trailer not have a charger built in? Mine looks like this one:
http://www.campingworld.com/shopping...mp-brown/74212
Basically it takes the power from your battery and distributes it to the devices inside; and also when plugged in gives you power to charge the battery.
For testing, you want a digital multimeter. Canadian Tire will often have one on
around $10 (Not sure if that one is any good or not.)
What you are looking for is as follows when connected to your battery:
> 12.9 volts- it's charging the battery. Typically charging voltage will be 13.5 to 14 volts
12.5 to 12.7 volts- fully charged battery
11.75- 12 volts- time to look at recharging the battery
11.5 volts- minimum I ever let my battery get to.
<= 11 volts- you are risking permanent damage to your battery by going this low.
I am also curious where that 2nd wire coming off the positive post is going. Could be something that is draining the battery.
As for DIY replacement of that fuse- I would say it's easy. Keep in mind that unlike speaker wire you have thousands of times more electrons squeezing through those wires, so make sure your connections are solid.