I would never mop up dog hair, I would vacuum first then mop. All that dog hair would be a mess if you washed the mop no matter what kind you used. It would be in your washer also.

I have found no vacuum that gets all pet hair.

I don't have any suggestions to offer, but I don't think any microfiber mop is going to release dog hair. Have you tried the PVA sponge mops?

Do you mean polyvinyl alcohol? Odd concept.
I found these guys or were u referring to something else?

Here is a link that might be useful: PVA mops

When I want to clean my linoleum kitchen floor, I sweep first (a "must" with four people, various crumbs,cat and dog) then damp-mop with a sponge mop dipped in any detergent solution (I currently use Top Job). The sponge heads are easily replaced.

I recently got a Rubbermaid Reveal mop and find it to be sturdy and well made. Its thick microfiber heads are excellent quality; they have a good scrubbing texture and absorb a lot. It's exactly what I was looking for. The 16.5" size is big enough to clean large rooms quickly, but still maneuverable for small rooms, under the kitchen table, etc.

The Rubbermaid Reveal has a one-year warranty. They reserve the right to require you to ship the mop back, but it sounds like a phone call with description of the problem, and possibly a photograph, is usually enough to get warranty repair/replacement. I'm not worried about it; if it malfunctions soon, hopefully I'll get a warranty replacement. Otherwise, if I got a couple years' use out of it, considering the cost, that would be fine. It's not an investment like a Miele vacuum or something.

My old sponge mops are headed for the trash. They stay far too wet after wringing. And sponges don't grab onto dirt or bacteria like microfiber does.