
Whether it would have been best to start on neutral ground or in the home depends entirely on the dogs - I always find introducing at home much easier, but then I always have at least one dog that's got dog issues (I take on dogs with issues) so out on a walk, they would already be on edge looking for 'danger'. My current problem dog takes a minimum of 2 full weeks to adjust to a newcomer so a walk on neutral ground would be a waste of time and more likely to totally scupper any attempt to get them living together!
In any case Missy is home now, so you've just got to work with what you've got. I would separate and give Missy time to adjust to her new surroundings, new rules, new people, new smells, new dog etc with minimal stress. While she's separate you can still work on things - reward both dogs for any good interactions with each other through a gate, and by 'any good interactions' I mean everything from glancing at each other without being bothered or even ignoring each other as they move around their individual areas. This will start to build a positive association with each other ('the new dog = food, yay!') which will make it a lot easier when you do try to introduce them again.
When you do get to that point, take it carefully and remove all possible triggers - toys, chews, even beds to begin with and possibly even stay on your feet, moving around calmly, if there's any hint of your old girl (or indeed Missy) guarding you. Harder to guard a moving target and if you're mobile, you can watch their body language and step inbetween them to break eye contact if necessary, or lead one or other away if tension sets in.
Also, don't panic! The first days and weeks are often the hardest as all parties are learning about each other's reactions, behaviour, quirks and foibles. Just take it steady, maintain the ability to separate immediately if required (stair gates, crates) and keep on rewarding the good stuff once they are together. For safety I would also be separating while you go out, once they are together, at least for a while.