Sorry I missed the 4 legged question..you could go around the old arboretum in an hour and the restaurant/cafe is close by and is dog friendly..so if there are 2 of you you could tag team it.. would be a shame to miss the old arboretum completely.
One other thing..there is a weekly video clip on the friends of Westonbirt website showing the current state of play (I found out after my too early blunder towards the end of April) ..but not a great deal of help if you’re planning well in advance
Or the dog could have a couple of hours kip in the car, temps are unlikely to be dog unfriendly at that time of year, plus there are big trees near the car park so should be possible to park in shade for part of the day. (I would like at least two hours in the old arboretum! Westonbirt really needs a full day and even then you will go away and realise you missed something you wanted to see... and agree with @dicky5ash that you can do Batsford in 3 or 4 hours as long as you don't mind walking uphill!)
That's great advice, thanks guys! Yes I expect we'll plan a full day at Westonbirt. Visits like this are always so weather dependent, but first week of May sounds like a good bet. Of course many other factors will determine the actual date. But since I've never been, I'm really looking forward.