Can you get coronavirus from drinking from family members mugs ?

I think it's possible, but nothing like that has been proved. Go ahead and drink. If they have it, you'll get it from their spewing when you make them laugh.

Only if they have it and you do it fast enough.

According to the latest briefing released by the World Health Organisation, the answer is “No”. 

https://www.who.int/news-room/commentaries/detail/...

CV-19 appears to be spread exclusively by inhalation of airborne droplets containing a large enough load of virus particles to cause infection. 

Pregnant women who have given birth whilst suffering heavily from CV-19 have never delivered babies infected with CV-19, and as long as the baby is separated from the mother until she has beaten the virus, the baby will not contact CV-19 even if fed colostrum and then milk expressed by the still-infected mother.

Thats a possibly if it's not been cleaned 

COVID has yet to be shown as living on other surfaces, but why tempt fate just to be a New Statistic?

Yes it is possible