Tudor is a nice site well situated for your choice of destinations. Pub next door can be a bit busy in peak season but food and service has been good when we have visited.
Don't recall it having a play area though and pitches have EHU only not fully serviced.
Generally there are more sites a little further south of Bristol and have a better range of services.
Dulhorn Farm is close (but not too close to the M5) between Junctions 21 & 22. Nice friendly site, no serviced pitches, play areas, local amenities are a short drive away but not really walkable.
Amazing family weekend with old steam engines, classic car displays, market stalls, and full catering and bar. And camping on site - Save £25 by booking in advance.