Cool, it wasn't clear if you were tweaking in Sigil after creating in InDesign.
Problem with that is if you're creating an ePub for anything other than iBooks or conversion to Kindle, it's most likely that the reader is going to be using an ADE engine, so ADE is what you would use for proofing.
With regards to the odd spacing, without seeing the underlying code I would guess there is something in the CSS that is not supported in ePub/ADE but works in Sigil's book view (Sigil's rendering engine supports things that are not in the ePub spec). You'll have to take a look at the code to see if you can find what's causing it.