Interesting... I'm not sure what you're gaining really by running it through an irig then as you're just passing the audio through another device (the irig) before going to your computer. I guess if that's all you had on hand then it serves as your adapter, but if I understand you correctly and you just ran a 1/4" cable out of your module into the computer using a 1/4" to headphone adapter you'd accomplish the same thing.
Anyway, I think you'll have issues balancing the sound between your drum set and his amp running through an irig and a splitter. I think getting an inexpensive audio interface would be a better bet, if you can afford it:
That interface will plug into your PC via USB, and you and your uncle can plug into the interface. As long as you set audacity to record from that interface, it'll work great (and will likely be better sound quality than what you'd have otherwise). The audio interface is basically its own sound card, so it handles all of the processing. If you ever decide to use your drum set as a midi controller to play drums through software on your pc (using software like EZDrummer or Addictive Drums) you'll want an audio interface like this anyway for best results.
My 2nd choice would be to get a mixer, and run the output to your computer. It'll give you better control between the two instruments before it gets to your computer, but it might not sound great:
A small audio mixer, like this one: https://www.amazon.com/Alto-Professional-ZMX52-5-Channel-Channel/dp/B004TM31QK/ref=mp_s_a_1_8?dchild=1&keywords=audio+mixer&qid=1597440265&sprefix=audio+mix&sr=8-8
But see if you have a friend that can lend you one first, the box you have is a passive selecter, the mixer may solve the problem.
Try maybe also unplugging the computer from the power if it's a laptop.