Sounds like he could be feeling awfully territorial about his crate and feels he has the right to snap at you for getting in his space - could that be it? If that's the case, a regimen of obedience training so he realised his rightful place in your household would make a BIG change in his behaviour. Dogs are like little kids; they need and feel secure with rules and structure in their lives! And they truly love their leaders, so don't feel like you are being mean to him by imposing very firm rules; often overall behaviour will change when the dog is trained. Do an internet search on "NILIF" (Nothing In Life Is Fee), you'll get some good ideas. Terrier mixes can be very opinionated!
I have Rottweilers, and one is an EXTREMELY hard headed and dominant rescue. On the rare occasions he tries to challenge me, I don't punish him (he'd win!) I DO snap on his training pinch collar, and march him through some polite leash walking, sits, downs & stays...just to establish that he is NOT in charge. Dutch is also never allowed on furniture, he must wait for permission to go through doors or in & out of cars, and he must sit or down for any treats or meals. Without these ground rules, he could be a dangerous dog - with rules, he is loving and obedient (most of the time!) Your dog is lots smaller and you don't have to be so draconian, but for sure rules are extremely important to dogs and they are happier when they don't feel like they have to challenge or defend themselves or their stuff.
There's a fabulous author named Jean Donaldson - if you can get a copy of "Mine" or "Culture Clash" it would be well worth your time. In fact I think everyone who owns a dog should read "Culture Clash" it's an amazing book about understanding dog behaviour and a very easy read.
Cooper The WonderDog
Daphne The Destructo-Rott