"Watching Chelsea mother [granddaughter] Charlotte is just the greatest joy," Hillary, 68, said in one video, Chelsea at her side.
"And I also occasionally feel a little bit happy that I kind of see something coming back that I maybe did or said," Hillary said.
For Charlotte's future, Chelsea, 36, said she wishes "the same gift of imagination and kind of sense of possibility that my mom gave me."
"It's hard though, I will say, when you are a mother for the first time," Hillary chimed in.
She shared this story: When Chelsea was very small, and "crying and crying all night," Hillary said she "couldn't figure out what to do."
"I was really getting upset and frustrated so I was holding her and I was rocking her," Hillary said, and I said to her, 'Chelsea, you've never been a baby before, and I've never been a mother before. We are just going to have to work this out.' "
Meanwhile, Hillary got a little bit of an early Mother's Day present herself on Saturday when she won the Guam Democratic caucuses with 60 percent of the vote, earning her four of the seven delegates at stake as the primary process winds toward its summer conclusion.
Presidential rival Bernie Sanders will pick up three delegates from the caucuses, according to the Associated Press.