Wow can I relate to you. I've had to take dogs like this from their owners and do boot camps to fix this problem because for various reasons they couldn't. Food and praise has nothing to do with this lesson in any shape or form. This could be why the problem has not gone away.
First off: Keep your sense of humour and patience.
(I know it's very tough by now! And it's really rough when it's a high pitched cry as it grates. I sympathize.)
Exercise both mental and physical is excellent.
One question is why you say "during the day she wails from her crate"? How long and why is she kept in a crate during the day?
Second: You "have" to ignore her. Period. Any behaviour you ignore goes away. Remember how you behave when you are totally ignored? You give up as it doesn't get the result you wanted. This means no eye contact, no speaking to her, Nothing, as that is like teasing her. If she sees she has your attention in any way at all she will wail louder and longer as she thinks her methods are starting to work on you so if she just tries harder..... 'nuff said?
If you have to put a towel/blanket on the crate so she can't see you and the stimulus is reduced.
She must "cease to exist" when she wails, cries, whimpers.
She "must" be totally quiet for 10 whole minutes before she comes out. That means even one tiny whimper: the clock restarts. You'll have noticed she carries on for a while and then goes silent for a bit then just as you're thinking blessed silence (not 10 minutes I assure you, lol) has come...she starts up again.
This is normal. She tried wailing. hmm that didn't work. She silences while she thinks about it and now tries howling. When that doesn't work she tries whimpering. When that doesn't work she scrabbles at the crate door and barks. She is running through a repertoire to try and get the result she want. Let her. You have no choice.
If you've looked at her or spoken to her (reprimanding her?) given her "any" kind of attention you've inadvertently added to the problem. Even giving her heck is attention! Not what she wanted but it's attention!
You can put a toy, chew toy whatever with her.
Make sure you continue your life normally. Walk around, sit down while totally ignoring her. Often as you seem to be coming near her crate she quiets as she thinks you are finally obeying her. This is why you have to wait 10 minutes. Walk in and out of the room she is in many times to help her learn this. Pass on by the crate as she doesn't exist right? Help her learn clearly and as quick as possible that any kind of fussing doesn't work in any way.
I repeat: you must have 10 minutes of silence before she gets out of the crate or any attention. When you let her out do not make a fuss.
Be calm and kindly neutral.
I've done this techniques with literally hundreds of dogs of every age and it usually works within 24 to 48 hours. Only once did it take 3 days with a 2 yr old dog whose owners had treated the dog when it carried on so it had inadvertently been rewarded/trained to carry on. And they had looked at him and talked to him while he was crated so the behaviour had been very re-inforced by them. And he was a most stubborn dog, lol. But he learned and became a calm companion.
It sounds like she has or is on the way to separation anxiety. Whenever you come and go from the home (or a room) simply leave. No fuss, no talking or petting. Tell her your coming and going is normal and no danger involved. Tell her that by not making any issue of it. Dogs perceive a fuss made on them not as parting guilt but as you saying you are worried and going into danger. And the exuberant reunion as your relief at making it home safely. Safety of the pack is paramount so if you are "in danger" the dog will stress. When you come home, walk in, go about your business totally ignoring the dog for a few minutes till it calms down. Then have the love-up.
Look at how the dog will perceive it versus what you mean by it.
With you in spirit....
