I'm afraid it's not Rosacea, these are permanent brown bumps. I've looked at many medical encyclopedias online but they don't have pictures of this, but I know it's common enough.
Hi,
I haven't opened the link you put on your post. Also don't know where you live or why a dermatologist couldn't see your mom.
What I can share is that I've suffered from Rosacea (it can look like many things), an inherited skin condition since the day I turned 60.
It is a bacterial infection, so doctors recommend treating with antibiotics, taken orally. I am unable to tolerate the medication, so deal with it by applying lotion twice a day.
Hope this helps. You could look up the condition. I only mention it, as it can appear for first time after 50.