Greg,
Welcome!
Riding with the kids is a nice way to ride, I think.
My most commonly used bike for this is my commuter modified mid-90s Trek MTB. It has more of an upright position than my road bike so I can better see where everyone is, and I can make quick turns if one of my kids darts right in front of me. Such bikes abound on CL. Find one that fits you anddon't be afraid to hold out or the one.
Adam