Ailish, I'm pretty sure from your original post that the dog next door has caused the lapse in behaviour. It might not be the total reason, but I'd say it's certainly been the trigger. Particularly if the dog has urinated near your door.
It’s sometimes hard for us to remember, but most of a dog’s life is governed by what he smells, not so much by what he sees. Everything has a smell - not just objects and people, but our emotions and hormones as well. A dog's world is a veritable kaleidoscope of different smells, and that's how they get their information. Also, and I don't know if you knew this, a dog's nose is 10,000 times more sensitive than ours! Some dogs can even smell early cancer in sick patients, before medical testing will show it.
So, not only can your dog hear this new dog, but there is a new assault of smells to excite her. She can hear a potential `friend' or a potential `enemy' - at the very least an interruption of what she perceives to be her territory and her boundaries. And she can smell it ALL DAY. Something is new, she knows what it is, and she can't get near it.
She is frustrated, and the answer to his frustration is to revert to behaviours that weren't quite gone, although you thought they were. She's wrecking things, urinating again (territorial marking) she's running around in circles because there's something new and she can't DO anything about it! She's also excited and frustrated because there's a new dog in town and there's closed doors between them.
If possible, can you introduce the dogs? Perhaps approach your new neighbour and set up a play date or three? I think, if your dog is allowed to check out the competition, it will go a long way to easing her frustrations.
Secondly, I think crating is probably not a bad idea. We don't use crates in Australia, however I think that their value may be underrated. The crate won't be seen as a bad thing as long as you don't associate it with bad things. Crate your dog for 20 minutes or so while you're home, too, and randomly, so she gets used to it and doesn't feel like it's a punishment.
Baby gates are good ideas also - if she's a jumper, don't use a baby gate, but a larger piece of collapsible lattice - that's what we use for ours - you just need to make sure it doesn't collapse - if you can affix it to something that would be great. They're cheaper, too - ours was $20 from the local hardware store.
Make sure your dog is tired. If you normally walk at night, get up early and do it in the morning. Does she have toys? Or is she left at home to get up to her own mischeif. One or two good interactive toys (kongs etc) will go a long way to easing her boredom and therefore lessen her mischief.
A good hard rawhide chew or something similar will also keep her occupied for a long time.
I would try those things and see how you go.