This thread makes me very sad. In the absence of any evidence whatsoever, the father is being, essentially, accused of potentially being a threat to his daughter.
At that age, friends frequently compare living and family situations. In my experience most of their nonsense has to do with money. I suspect that your daughter's friends comments were in that vein. It seems to me unlikely it was based on any suggestion Dad was an an abuser.
The fact that your children's father spends so much with them is a bonus that will serve them well throughout life. It would be a terrible shame to ruin that relationship over this issue.
I agree entirely that pre teens need privacy, to change clothes, to look after their personal hygiene and to just chill out a bit. The situation at Dad's is not ideal of course.
But, unless there is evidence of something untoward, I do not think the Father is doing anything wrong. Families sleep in the same room all over the world. When traveling even affluent families share sleeping quarters.
I of course don't know how you relationship with your ex goes, but I would suggest now is a good time to get together and collaborate talk about how you are going to jointly parent your children as pre teens and teens. It is hard but worth it for your kids. You can do this for your children.
It is also the most important time for you and you ex not to speak ill of each other and to present a united front. Otherwise, "splitting" will be rampant.
Good luck.