Hi A.,
First of all, a great big hug for you (and a welcome into the world of parenting a deaf child)
I can tell you FROM EXPERIENCE that a deaf child can be disciplined and held to the same behavior expectations as any other child. The KEY is communication. Julie M is right about the Deaf community (in general) having a chip on their shoulder regarding communication barriers. The many who suggested sign language are absolutely right! It is ESSENTIAL that you learn signs. The better communication you have (via signing AND whatever else) with your child, the less of a chip on his shoulder he will have towards hearing people in general and your family in particular. I love hearing people but that is because my whole family signs and I did not have any barriers at home, only later when I went out into "the world" on my own.
Highly recommended videos (in addition to a class and/or hanging out with deaf people who sign with you - nothing is as good as this!) "Signing Time" videos are very good. The reason I say this is not because I have learned signs from this (I learned from my parents who are also deaf, and my son is learning from us who are also deaf) I have met people/friends who used signs pretty well and I knew they werent taking sign classes and that I wasn't teaching them. Every time it was from Signing Time. (Many other people try other videos but are still afraid to or just dont sign as well as those I've seen using Signing Time. I do NOT recommend books - they are ONLY to remind you of what you've learned - you cannot learn movements from a flat image)
There is so much I want to share with you but this may make it too long for you to read. Please feel free to contact me and I'd love to meet you if we can. At the very least, I can share with you the tricks and joys and perks of being Deaf!! ____@____.com
Even though I came from a deaf family, went through public school, deaf school, mainstreamed, all that, it was still a shock for me when my son became deaf around the time he turned 3. So while I can't say I understand totally how you feel with finding that your child is deaf, I do understand at least some of the emotions and all of the struggles (maybe even more, cuz I have seen so much?) of what to do, where do we go, how do we do this, all those questions.
A great resource is CRS - Childrens Rehabilitative Services - they're closer to you in Phoenix than they are to me. They are great in that they take care of all the testing and provide my son's hearing aids free. (They didn't help with the emotional/behavior aspects though, maybe because it had calmed down before I found them)
Your 3yo's tantrums are a mix of A) frustration in not being able to tell you what he wants B) wanting to be more independent than a 3yo is able, and C) just being a normal 3yo!
I didn't have the terrible two's with my son - I attribute that to us using signs and his being able to tell us when he was done, when he wanted more, if he wanted bananas or crackers, etc. But oh boy, I wasn't spared the trying three's!! He'd want to do things himself that I wasn't about to let a 3 year old do independently!
One more thing, if you're still reading down this far! Regarding the closed door -- what my parents did for us naughty deaf kids was to put an hook and eye on the top of the bedroom door. That way the door is not completely closed (if you can't hear what's on the other side, it is scary) but the child cannot come out. Do it so that the door is about an inch or two open, wide enough to see through. I did this with my son when he WOULD NOT EVER STAY IN BED, and only had to lock the door for about a week or two before we could simply put him to bed and he knew it meant to stay there. The first couple nights were hard and wrenching because he screamed and cried and shook the door so hard but the peace of mind of being able to put him to bed and have him stay there is SO worth it!!! 2-3 years later he's still good about staying at bedtime and I've never had to use the door latch since. (maybe once or twice for 15 mins)