The trick to handling the parents, I think, is to not change anything, but just explain your activities to them in educationalese.
For example:
Children practise their fine motor skills, focusing on pen control, and learn basic colour theory = Colouring.
Children learn to work together, with a focus on learning to differentiate between different tones and pitches, as well as different cultures = Music (if you're singing english nursery rhymes you could also add that they're practising their foreign language prounciation while they're at it).
If you can't have free flow between indoors and outdoors, you can at least have some sort of free flow between activities. What about a nature table to help children keep some kind of contact with the natural world?
Could you take the children on a walk at least? (I don't know where you're working, so obviously air quality and city crowding could well be an issue for you!)
Would it help at all for you to compare the way you want things to work to how things are done in Hong Kong, which has well established
Early Childhood Education training?
I would love to know some more details about your setting, I find the development of ECE in other countries fascinating.