ADVICE PLEASE!!

You guys know that I love to clean, yes love. Aaron says I use any excuse I can get to vacuum. I love it because I love seeing the finished project, and with two boys, it is a project!!! Well I have come upon a mess, that I can not defeat!!

We have linoleum in our kitchen, and it is a BEAST!!! I have had it in previous apartments, but have always been able to keep it clean. I use a swifer mop at least once a week, and about twice a month, I am on my hands and knees scrubbing it with hot water and soap. Two days after I scrub the floor, on my hands and knees, it is disgusting again! How can I tell? My boys knees, feet, and clothes. There feet and clothes are black, and I mean black. West's knees are also black. I am so tired of scrubbing the floor on my hands and knees!! I need help!! Does anyone have any advice, on how I can keep the floor clean? Please help!!!!!