It's hard to spend time with them knowing they'll be leaving soon, but that's the most important time to spend with them. When the best thing you can do for them is to make them comfortable and comfort them, let them know its okay to leave.

Something to remember is that animals do not fear death like we do.
I wish we were more like animals.

My prayers and thoughts are with Rudy and your cousin.
I pray Rudy's passing is peaceful.