Hi P.,
Your aunt sounds like my uncle.. Lol.. We just had the same thing happen on Saturday. My uncle came over with some toys, which personally I think that he picked up at a garage sale or just found somewhere. They were dirty and really needed a cleaning prior to my son touching them. This is how we cope with the situation whenever it has occurred.
First: We made it very clear to our friends and family that we like to clean all of his toys prior to giving them to him, even the new ones in boxes. (I know sounds a little maniacal, but we have become germaphobes).
Second: We request that all used toys be given to us in our hands and not his. When he is opening new gifts, we go with step 3.
Third: We have shown our son that toys need to be cleaned first and then we can play with them. At this point we usually have the Clorox Clean up Spray ready with paper towels and clean the toys in his presence.
For board books, we wipe down the covers and pages. If they are hand me downs, as long as you clean them, I don't see why kids can't have them.
Now if it's just that you find it disgusting to have hand me downs due to fear of not getting the items clean enough, express this to your loved ones. I think that anyone who knows you well enough and whom you have a strong relationship with should not find it insulting that you express your concerns. You could also suggest that due to the fact that you feel your daughter has enough, that if they want to visit your child, they do not need to bring a gift along.
Take care.
D.