There are far deeper needs than just the funeral. Her mother needs a new place to live now. I would never be able to go back to that place. Would you be able to work after your 6 year old was murdered? Money will give her time to grieve without the worry of supporting herself. If she wants to stay in bed all day, she can. If she wants to pay for therapy 3 times a week, she can. Just because the child is dead and she was her only child, does not mean there is not a need to support the mother.
Also, and I've said it once and I'll say it again: if you feel led to donate to her mother, you don't get to be judgemental about how funds are used. That's the whole point of giving without thought or reward for yourself. You realize this mother may need that $50 more than you right now and you don't get to judge her for it.
This is not directed at you per se, but to anyone in general who feels her mother does not deserve the money raised.