Teenagers are monsters. LOL
My son is 14 and does talk smart to me much more than he used to. When he crosses the line I warn him, then I begin taking privileges. I also tell him he doesn't have to like my decisions but I am the adult in charge so he has no option but to go along. I think we all struggle with this when our boys get to be teens.
As for the alarm thing - been there, done that last year. I told my son that I leave the house at 7:15. If he was not out the door with me, he was going to walk to school. Period. He had two days to get it together. The 2nd day I was heading out the door at 7:14, he ran down the hall to get something as I was walking out - I have never seen that boy move so fast in his entire life. 30 seconds flat and he was out the house, in the car and strapped in.
So, tell your son that if he cannot get it together in the morning he will be taking the bus to school. Period. Let him take the bus home or to a the teen center. If he goes to the teen center you pick him up at your convenience. Don't make things too easy for him. They do get to a point where they take us for granted - that's normal, but then it is time to show them how all the little things we do them make their life easier.
As for the Father denigrating you - you may need to have an honest conversation with your son about this. Tell him that you know Dad talks badly of you and you would hope that he would be grown enough to hear your side.
As for arguing in the car in front of the other children - just don't do it. No matter how annoyed you are with the 16 year old - wait until evening then talk to him alone. Arguing in front of the others is giving the power to the 16 year old - and you simply don't want to give him *your* power.
You could also try therapy - if your son is having difficulties balancing Mom and Dad, etc. this could really help. I have done this with my son and it really did help us improve our communication and helped him deal with other issues he was having. You could also seriously offer to have him go live with father. When mine thought he could get his way by saying he didn't want to live with me I offered to pack his things and drop him off at his Father's while I was picking up the phone to call his Father and let him know I dropping the boy off. He backed down very quickly from that one.
Mostly, be consistent. From what I hear they outgrow this and began human again in their 20s.