Severn Tunnel station is approx 2 hours to Paddington with plenty of (pretty sure it’s free) parking. This will all be five or ten minutes drive from some of the villages like Magor, Undy, Rogiet in South Wales but close driving distance (or train) to Cardiff and Bristol. The same train station has trains run through from Paddington to West Wales.
Forget Chepstow itself; the trains are not on the London line and the traffic very bad in the mornings. You’d have to drive to Bristol or back to Severn Tunnel to get trains to London and you’d have to allow minimum one hour drive to do that, possibly more for Bristol.
I’d suggest looking in the small towns and villages mentioned above; around the Chepstow/Magor/Caldicot/ Portskewett areas. You’ll get more for you money; I’d be amazed if you couldn’t pick up a decent sized property for that budget. As your daughter is musical, there are school buses from those areas to Wyedean School which is an excellent local Academy with a fantastic reputation for its music department.
Other option could be Thornbury with quick access to Parkway station. Again, lots of villages and small towns in South Glos, or even Cam or Dursley could work for you.
Expect prices to be slightly higher than South Wales if you do look at South Glos/ Stroud/Dursley. You can also get some good house prices around Gloucester; Cheltenham is more like London prices so steer clear.
I know all of these areas well and do sometimes commute to London with ease from this area.
Final thought; we put a purpose built standalone and soundproofed “pod” in our garden - originally intended for loud instrument practice. No planning required; consider that scenario as part of your options, as this could hugely widen your net.