Are we forbidden from [accepting] gifts given to us by a relative, knowing that they are stolen and bought for a paltry sum, and are we obligated to return them or not accept gifts from him in the future, while maintaining kinship ties?

If you know that the item of the gift is stolen, then it is not permissible to benefit from it, and it must be returned to its owners if possible, for the one who takes from the usurper or the thief is the same as long as he knows that the money is stolen.

And if you obtain something like that as a gift, do not return it to the one who gifted it to you, but rather return it to its owner if he is known. If you do not know its owner, then give it in charity on his behalf.

As for what you do not know to be unlawful from what your relative gifts, there is no harm upon you in using it and benefiting from it, based on the principle that what is in the Muslim's possession is his property.