My boys are teenagers but we still have family time, it's amazing the things you discover about your children when they are relaxed.
We spend a great deal of time in the car driving to sports activities and we share music to pass the time. The discussions are awesome.
My son is 15 so he's at the age where he'd rather spend time with his friends and practice for sports. But, I still tuck him in the nights he's with me. Because this has been our routine since he was an infant, we both go into 'relaxed' mode and he tells me things then.
Also when we're driving. Something about driving that he opens up and tells (or asks) me the most amazing things. One I'll never forget was when he was about 11, a 6 hr trip where he'd put his jacket over his head for an hour or so (I thought he was asleep) when he took the jacket off and asked "mom, why does girls hair smell so good?" Took all my self control to not laugh and I calmly replied "because they wash it". He thought that was a good answer.
this is off topic but son just came back to me last night after being with his dad for awhile. I couldn't help looking in on him a couple times this morning while he sleeps. Doesn't your heart just about burst when you see your kid(s) sleeping peacefully?