I don't think you were being unreasonable at all - and I say that as someone who doesn't have my own kids. I'd still hope most people with any sense and compassion, with or without kids, would be sympathetic towards someone whose little 'un is cutting a tooth - and it doesn't sound as if the soundproofing in those cottages was particularly good either if the people next door could hear you all that well, unless it's, you know, in the middle of Dartmoor or somewhere, where every tiny sound carries.
Also, always love all the comments from people who think we should all be able to predict the future, down to the minute a baby starts to cut a tooth, and basically that new mums/dads/carers and their kids should stick themselves in a kind of purdah until a time deemed appropriate by such people....! Years ago I worked in Ireland and when one of my colleagues and I got too b*tchy about anything in particular we had a particular phrase we'd use to stop us in our tracks - it was along the lines of, "Aye, if only everybody else was as perfect as us...." At which point we'd burst out laughing and have some cake or a sticky bun. Usually with tea.
Seriously, if the owner's that bothered, why doesn't she do what some campsites do and make it obvious that it's an "adults only" complex she's running and that actually she doesn't want pesky families with kids who might - oh my God - make a bit of noise, either playing, or grizzling, or, you know, just growing up in general? (Though she might get a few different issues to deal with if she marked it "adults only" of course....) Or, alternatively, add a notice that says "impeccably controlled, preferably silent, children and families welcome".
Ye Gods at her behaviour. Hope your little 'un is doing okay (and you too).