Sounds to me as if the OP is using an amp with an xlr, or 1/4" out that has a speaker emulated ( or perhaps not ? ) output. Many guitarists these days are taking the modern approach of using modeling amps to create a large range of tones. Some use a split to send sound to FOH and to a monitor of their own in order to keep levels down. If it is in fact a send from the amp he would need some way to isolate both sides if an issue does arise.
Here are the facts.
OP has:
An AMP with some form of sound output for FOH use.
Needs to split between FOH and a " personal monitor ".
Will not be micing the guitar amp.
Being a guitarist myself ( as well as a sound company owner ) I would bet that the OP needs to split sound from the AMP/MODELER ( can be both in the same box ) to get sound where he needs it. To me that should be a Y at the amp/modeler and a DI used for the send to FOH. I would use a lower priced Di for the monitor side too if noise becomes introduced on both sides.