The great dandelion wars!

I don't know about you, but I dislike conflict of any kind.  However, I have this recurring pest in my yard that makes me want to pull out all my hair.  Yes, they are kind of cute with a sunny yellow flower, but they are the enemy!  This year they are so prolific, that my back yard is a sea of yellow.  As you may know, I use a push mower.  All the stems do is lay down as I push through them.  This causes me to have to mow the lawn 3 different ways just trying to cut the majority of them down, then I go back and pull off the rest.  This drives me crazy!  On top of that, I have a small garden, so I don't want to poison them, honestly, I don't think I could anyway.  I am the person who takes a spider out of the house with a paper and a cup.  So here we are, again.  I guess I should be grateful I don't live in California right now (Sorry California)  I would probably miss the little buggers.....NOT!