Best coast 2 coast route for young children

Hi, I'm wandering if someone could advise a coast 2 coast route going west to east that avoids roads and nothing to technical off road. I plan on doing it during the Easter holidays weather permitting with my son and I have only done road routes before, having a few close calls with cars I don't want my son on or near the roads really when doing it, especially as he's only 6 and the bars are quite wide on his bike. He's pretty good off road and climbing and descending hills so was thinking of doing the Hadrian's wall route, modifying the end to finish in newbiggin by the sea as we live nearby, has anyone done this route that could tell me what it's like, or one that could be better for me and my son.