Haha yeah it does seem a little gross but here's what I do that helps.
Shake out everything really well outside (or in your garage or something and then just sweep it up afterwards), you can also get a rubber brush to get most of the hair off, then put everything in pillow cases or a mesh washing bag to cut down on the amount of hair that gets in the machine. I use half a cup of detergent, a teeny tiny squirt of blue dawn and a capful of bleach. That gets rid of the smell and also... Whatever comes out of a little guinea pig is no match for detergent and bleach I'm just sayin haha. You can use more than a capful of bleach if you need but it just depends on how good your washing machine is. What you do not want is to open up the washing machine and smell bleach. Even with just two capfuls I have to give it an extra rinse cycle. So start with one capful and go from there, you'll figure it out.
Also if it will help your Mom be less grossed out lol you can do an empty bleach load after you're done with pig laundry just to thoroughly clean the machine...