Personally I think I'd want to keep it separate altogether, including the name and start afresh, not with just another version of the same name. To me the main thing would be that all the family that wanted somewhere to gather and use would be together.
Instead of for example, smith.com, you could try something like changing it to thesmiths, thesmithhangout or thesmithfamily. Something that would still incorporate the family name but dissimilar enough to avoid having anyone getting in touch with your website looking for him, for instance.
I guess it depends on what kind of relationship you have with him now whether you'd want to remove any chance of association with the man or not.