NOTICE: YOU DESCRIBE A DANGEROUS CONDITION EXISTING WITH YOUR TRAILER. Someone can get electrocuted just touching any metal on your trailer.
This condition indicates that your 120 volt wiring is not correct. Start at the place the shore cord is plugged in. Make sure that outlet is wired correctly. I can't say exactly what "correctly" is because I don't know how you obtain the 120V. It can be a 15 amp duplex outlet with an adapter to a 30A RV, or it can be a 30A RV outlet. Also make sure the plug which is on the cord to the trailer is wired correctly. If it has been changed, it may be wired incorrectly.
Also check the wiring going into the power panel inside the trailer. You will need to remove the panel around the circuit breakers. There should be 3 wires, green going to the ground strip mounted fast on the side of the panel and where all the bare copper wires connect, white going to the insulated strip which is AC neutral and where all the white wires connect , and black going to the main breaker.
Your condition described as "an electrical charge" is a VERY DANGEROUS condition. Someone can get electrocuted and thus being fatal. If you aren't comfortable doing this type of work and diagnostics, then get the trailer to someone or some place to get the matter corrected. If you THINK you know what you are doing, this is not good enough. You must KNOW what you are doing and what is right and what is wrong.
Fuses blow for a reason. There is too much current flowing through the circuit. DO NOT install a larger rated fuse.
"My fuses seem to blow more often than they should, going back some time.
Just by chance, I noticed, while gripping one of the stabilizer jacks. that it felt like it had an electrical charge. So now I suspect that something somewhere is shorting to the frame. I don't know where to start looking. Any ideas?"
Clearly, you need professional assistance to resolve this issue.