When my kids were young, my ex and I had split custody. For at least half of those years I paid him child support. We all did just fine.
I have to admit one of the reasons I was always insistent on having a career was that I never wanted to be in the position where I could not take care of myself and my kids without a man around. Even when my first marriage (which lasted 18 yrs) was in great shape, I could not allow myself to be dependent on him.