Yes - it does sound like your dog is exhibiting this kind of behavior out of frustration.
If he's previously had free run of your house since he was one year old, all that crate-training you did with him when he was a puppy is pretty much out the window at this point; especially if you're suddenly throwing him into his crate for longer periods in the day while you're at work.
Another problem is all the changes it sounds like your dog has gone through lately. New person in the house, new environment, and now - new rules.
Unfortunatley you cannot 'reason' with your dog. They need to be shown consistancy.
Because you own a dog that is a mix of two high energy breeds, it also doesn't really sound like he's getting enough excercise to mentally stimulate him for the times that he needs to be alone.
Can you hire a dog walker? Drop your dog off at daycare for mornings or afternoons?
"If you are a dog and your owner suggests that you wear a sweater. . . suggest that he wear a tail."
Vali (American Bulldog)
Artiro (Cane Corso)