Traveling through the garden might be hard as the paths are narrow is some areas. Other areas there is plenty of room.
I saw a lady pushing her kid in a stroller while we was there. But there is the one step, which you can take another path to go around and avoid it.
There are lovely brick paths.
There are many gravel paths and only one place with a step. The gift shop has no stairs but it is only open Fri, Sat and Sun. So yes I believe it is accessible.
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