In reply to Philip:
Another vote for the Welsh border area, you've got a huge number of quiet road/off-road options and it's beautiful countryside. It's relatively hilly between Shrewsbury and Ludlow, you could plot a route that avoided the worst of them but the very flattest roads tend to be the main roads. With the exception of the A49, these aren't bad to cycle on and I'd happily use them for short sections with our kids (youngest is now 10).
If you stayed on the train to Leominster (1 stop south of Ludlow) the land flattens out a bit and you would be able to get to Hay-on-Wye on pretty flat roads which would be about 40k. If your kid was up for one big day you could then go over Gospel Pass (note, this is a lot of climbing, but an amazing road) and finish at Abergavenny (30km ish). Third day you could find a pretty flat route to Hereford and catch the train back (same line as Leominster). If they're really not up for Gospel Pass, you could plot a flatter route round the east side of the Black Mountains for the second day.
I'm happy to help narrow down route details, I'm good on the Ludlow area, but will be more patchy as you head further south. As a starting point, here's a ride from Hay to our house https://www.strava.com/routes/21430400. I think of this as a pretty flat ride for the area, it would be easy to tweak the route for a Ludlow/Leominster start.