I've only won a few lower prizes, but had a colleague who won a large prize. He tried to help those needy relatives etc, and bought a stake in a business.
When the bubble burst, and the economy downturned at the beginning of 2000, he was the one who needed help to keep his house(Bussiness gone, family broken and no job). The people he had helped were ok by then... Good jobs etc, and they told him "we sure have the money to help You, but it's not like we won in lotto or anything" And they couln't find the (little) money to help him.
Moral of the (true)story... These distant relatives feel entitled to the prize, because they are family, but they won't feel entitled to help You if the situation is reversed.
If they are in trouble, it is most likely because they overstretched their economy, spent too much of their earnings etc. If You pour money their way, they won't see the incredible generousity that You are displaying, but just say "whew, disaster avoided, I feel like spending some money".
Just a few thoughts from someone who has seen it firsthand.