Best heavy duty floor mop?

Help me out ladies. We have 3 large dogs, 2 cats, our home is surrounded by mud, snow, ice, and puddles. My floors, walls, doors, and baseboards are DESTROYED within 15 minutes of a deep clean despite me trying to keep the animals clean too. I’ve been through so many mops, and none of them seem to REALLY get stuff cleaned. I always end up having to get down on my hands and knees and scrub the floors with a freaking towel. I homeschool my 4 year old, have a lot of other stuff to attend to as well (laundry, dishes, cooking, other cleaning, other animals such as poultry, horses, livestock, etc) and have a very high maintenance (but adorable) 16 month old, too.

I want a mop that WORKS.

So drop your recommendations below and If you have one that can be swiped across the walls and baseboards for a basic clean, that would also be amazing, but it ain’t necessary!

Thanks ladies!!