How do we tell mom who has dementia that it's time to sell her/our family home?

Telling her about selling the family home may be nearly as traumatic as telling about the death of a family member. She's likely to consider this a huge loss. However, she will likely what you told her very quickly. She will still ask to go home.
Some people would feel okay with selling the home and just not telling her, but I gather that you’d feel guilty for not being honest. So, my suggestion would be, for the sake of honesty, bite the bullet and tell her one time that the home must be sold, and that the money from the sale will be there for her comfort and care. Be sympathetic with her grief, but remind her that life changes.
Then, move on. If she continues to want to go home, particularly when sundowning, try to distract her, but I wouldn't keep telling her that the home has been sold. Here's my reasoning. Your mother will be put through the grief of the loss as though it's fresh each time you tell her the story. She won't likely have stored the memory of the last time you told her. To me, there's no point in putting our loved ones' through this repeatedly.
Telling her once is fine. Then you have been honest and shared this important fact. After that, you - and she - will likely be better off avoiding the issue. One thing to remember is that when she is sundowning and wanting to "go home," she may actually want to go to her childhood home. She may be beyond remembering her adult home. She needs comforting. She needs to feel safe as she would at "home." But the building itself really isn't the issue.
No matter what you do, her wanting to go home will be heartbreaking. This is a very common issue with Alzheimer’s. You can’t possibly provide whatever she really wants other than comfort, so leave the guilt behind and use distraction and re-direction techniques when possible. If they don’t work, hold her, tell her you understand her distress but that her last home is in the past and her current home is in the present. Get her through it the best you can and move forward.
This is painful, I know. Dementia is painful to witness when we would do anything to help or loved one but we are powerless to do so. My condolences.
Carol

Have you ever with her as a family about the eventuality of having to sell the family home? If you have, that would be best case scenario probably. We are going to have to do this eventually for my husband's mom. However, we have been talking to her all along about us being glad she had that 'money in the bank' so to speak for her care, thru the sale of her home. I guess if I were you, I'd put a positive spin on selling the house, because it IS wonderful that she'll have that money for her care so that the family isn't burdened. Since she's sun-downing, don't talk about this stuff except in the early morning. Maybe by breaking in the subject now, it'll be easier when the hammer falls finally. I hope you or someone else has the legal ability to sell the house if mom gets too far gone with her memory also.