They'll love it and so will the kids. You can sit in the background, inconspicuously taking notes. Don't try to record these sessions unless yours is a remarkably orderly and disciplined family. It takes very little background noise to drown out the voice you want to listen to on the tape. The same principles apply for video cameras - you need to be free from distracting noises.
Most subjects become a bit stiff and formal in front of a tape recorder or video camera.
Some even freeze up a bit when someone starts taking notes. You might want to consider stashing the notebook and just getting a story or two out of your relative. Then, slip away and write down their stories in privacy. At the other extreme are formal interviews for which you write down questions ahead of time and plot your strategy. Usually in these instances, you are starting from a plateau of significant knowledge and want to corroborate stories, flesh them out or seek new information.