Single Parents

My DD's father and I are divorced. Have been for 2.5 yrs now, and everything seems fine, until lately. We have joint custody, but I am very sick and not always physically capable of taking care of my child, so the agreement was, he keeps her, and I have visitation. This works out, as I know I am not a completely great mother. I'm not looking for pity, this is a fact and I accept it.
To make a super long story, as short as possible, I made this mistake of watching Stepmom last night, and can't help but wonder if maybe my kid would be better off without me. I am in fact very sick, not something anyone can catch, but sick. I've died on an operating table in the last year, and know for a fact I'm lucky to still be here, and to have the miracle child I was never supposed to have (per doctors). With my illness comes alot of down time and not alot of up being a super mom (like her stepmother). I feel like I'm screwing her up. Her school seems to be suffering this week, not bad, just enough I'm concerned, and she seems alot sadder lately, than is normal for my more uppity bright sided 8 year old. I've made her cry alot lately being in so much pain and instead of talking things out with her I yell which isn't her fault, it's mine.
I suck at being a parent, I know for a fact I do. I just want to know how some divorced parents handle not being around your child, but in the same sense, knowing you really aren't the best parent for them to be with. I know she loves me, and tells me all the time I'm the best mommy ever...just can't help but think that it isn't fair to her to have to survive me as a mother.