Is it true that a divorced woman over 30 will never find a companion?

Well that is her experience. Rather blunt. But, probably truthful ish. But it is not set in stone. Having three kids does present an initial hurdle and could be too daunting for some men. But some men want a built in family. Good men... not weirdos. So get out, think positive, try to meet men in respectable places and get to know them and they you before you sleep with them. No bringing them home to meet the kids until you are a couple. Meanwhile prepare your kids and set expectations for them as to how they will behave and what this person means to you and them.