I'm sorry to hear about this and I know how upsetting it can be. Of course you're not a horrible mother ;-) this is just what angry children say - all over the world!
Never the less
''my husband and I just let him do what he wishes so he WONT get angry''
This is the WORST thing you can do!
You may need professional support for a while to know how else to cope with this as a couple - and (basically) how to stand up for yourself, stop being manipulated, and tell him to 'stick a sock in it'!
He better not dare speak to you like that once you stop letting him rule the roost and start
a) ignoring the tantrums and insults and doing what YOU think is best without watching him for reactions
b) punishing him when it goes to far
... because if this goes on, guess what?
He will become an abusive man.
''My mother in law thinks that if we have another child his temper will mellow down and his attitude will change.''
What possible basis does she have for making a statement like this?
I'm positive one thing that will be true - you will have less energy and motivation to deal with him when you have your hands full with a sleepless baby.
Really, get some PROFESSIONAL advice. GOOD LUCK!
;-)