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Back to the OP - painting satinwood, or any wood finish directly on top of an unstable emulsion base is not recommended but removal will be a lot of hard work. Sometimes you can get away with it, sometimes you can't, so my advice would be to try one side of an inconspicuous door and allow it to dry for several days. If it seems fine then it may be ok to 'risk it for a biscuit'!
If this doesn't work, you can either remove it all or try using a primer like Zinsser Peel Stop.
http://www.zinsseruk.com/product/peel-stop/