Ancestry has a sister site called MyFamily that is very much like what you describe below, and it is free. You have to approve who can view your trees, etc, and signing up for passwords by guests viewers is required.

I've become disenchanted with putting my trees on Ancestry because if you leave them as "public" anyone can just pull your information over to their trees, and there is so much corrupted information in their databases now.

As an example, somebody trolling Ancestry pulled all the information on my maternal grandfather, Jose Marquez, all his ancestors, and added them to their tree. I know that the person who did it also had a grandfather by that name in another county in NM, and upon further investigation of her parents, I found a cousin of hers who had the correct information on their Jose Marquez. I have tried to contact the person who pulled my grandfather's information through the Ancestry system, but they do not respond. I have cousins who are diligent researchers