I can see why you want to. I still don't think you should.
I walk to work up a narrow pavement. It is so narrow I choose to never walk my children on it, if I am with them we go another way - it is really two people wide, so you can pass another pedestrian but not much more. It has two schools on it so is quite busy. Today, a cyclist was coming down the same path as I walked up and looked really cross at all us pedestrians being there. Thing is, it is a terrible, narrow road as well as a terrible, narrow pavement. I would not want to cycle it - so I don't. He needed to go another way, and so do you.
When my children and I cycle we:
(1) chose cycle paths
(2) chose roads where the pavement is wide enough and quiet enough that they can safely be on the pavement while I go on the road beside (I do not join them on the pavement)
(3) walk or bus instead
They are trained that on the park cycle routes, they stop or (if safe) go off the path if a pedestrian is near. On the pavement, they walk their bikes if there are any pedestrians - we live on a long, quiet road so they can usually see the whole route so we know whether it is clear or not, usually we pass no-one. The 11-year-old is now never allowed on the pavement, the seven-year-old still sometimes is.
It is frustrating that there are so few decent cycle paths in our area. I wish there were more as there are so many more journeys that would work well on bike if there were better provision. But there isn't - you can't just ignore the law and other road users.