How much does risk of cancer increase from exposure to polyurethane fumes? when and how should we start screening kids for cancer due to the exposure?

Hard to quantify: depends on how much exposure, for how long. For typical household refinishing floors and letting things air out before you come back in house, probably pretty hard to say there's a direct link or need for rapid screening. if there is a more prolonged and heavy exposure, would be a good idea to see what you can do to reduce it and consider talking with your kids' doc.