Monica,
All I can offer is to be brave, and focus on what you are reading. Take the time as you take a breath to look around the room, without actually looking AT anyone. This technique is useful for any public speaking, but especially so for such a sad occasion.
I have had to do two eulogies in my time. My grandmother's was a little easier, if that's possible, as she was 97, and had been in an hospice for some time. The upsetting thing for me was that none of her children, my older brother, and my older cousins would get up and speak. I thought this was terrible, so I offered to do it.
My mother-in-law passed away suddenly last year, and once again family members all shied away from speaking. I thought it appropriate to do it myself, as I actually worked with her before she became my mother-in-law, so I had a unique perspective. Unlike my grandmother's eulogy, I could not find the right words to write, so on the day I simply stood up and spoke from the heart. I think this helped me get through it as well.
Whatever you do, good luck in what is a difficult task.
Darren