you have never (quite rightly) explained why the new baby will be at such risk from the mum, but i can see your niece's mother's point. If the new girlfriend is such a risk that a new baby was that close to being taken away on day 1 i don't think i'd want my daughter having the chance of being around her, which in all honesty is what could happen at the moment from her POV.
I think your idea of going out for coffee/lunch with BOTH of them is a good one (and Banning talk of the dad during this time) and the idea of writing with this idea sounds like the only way of doing it.
I think hanging around in the street to see her is a very very bad idea - the niece is bound to mention she's seen you and it would absolutely ruin everything that you have been so sneaky