What recording program are you using? What recording equipment (sound card) ?
Every program I have ever used allows setting up a mono channel for recording. That mono channel is then panned in the middle, equally loud in both channels. To me it sounds daft to use splitters and things like that.
Monitoring of the sound could be either in hardware or in your program. Many soundcards has some kind of "direct monitoring" function, where the monitoring of sound is done in hardware. The reason is that going into the computer and out again can take enough time to be noticeable, this is called latency. Other solutions often used are to have a small mixer and creating the monitoring function there.
Gunnar