It's really nice that you want to help others. Also, I'm sorry for your loss. But there must have been a communication breakdown somewhere. Hospice is a great service, but they have to be requested by the family. It's not something that kicks in automatically when someone is dying.
Also, don't make this harder on yourself by assuming your mom's death was much worse than it should have been, and then blaming yourself for it. You don't say what she died of, but with more common illnesses like cancer, it's always difficult, and hospice can't fully change that. The most important thing is having a loved one there with you, and you made sure she got that.
I lost my mom when I was 21 and it was horrible. I remember one time I noticed her lips were so dry and cracked, and I wanted to give her ice chips. But the nurse explained to me why she couldn't have them.