I often hear parents complain when their children go through a clinging stage.
About 40 years ago I read a story in a magazine (I don't know which one) about a mother who wanted to push her clingy daughter away to help her be more independent. Then the mother went to a fortuneteller who told her she had only a year to live. The mother wanted to cling to her daughter so much that pretty soon her daughter was pushing her away.
You might want to try holding and hugging your children until they get their fill.