Sorry - just a thought....so 'the neighbour' got a previous tenant removed?
I wonder if it might be worth pre-empting her, and contacting your Housing Association yourself? Explain what's happening - point out her 'previous' - get a letter from your 'nice neighbour' if she would do that for you? I bet that 'lady' has quite the history....!!!
Plus, as the others have said, whatever pressure you're under from your partner etc...it's just not worth the risk. Our littlies can, in the blink of an eye, just take off on a whim. Until you have total recall of Oscar - please reconsider Flexileads/long training leads etc....better safe than extremely sorry xx