The weed is a factor here. it can be stopped.
Then you could see what kind of person she could be. But that's down to her. Not a single person on earth will be able to make her. Not even her own children are enough for her to make the choice to stop.
Thing is, these kinds of drugs are usually taken low level over time, but to sustain the effect the user is needing, more will need to be taken.
The angry/agressive trait could be a bi-product of this, but could be intrinsic to her too. Either way, angry/agressive parents are shit parents and ones that destroy children's self esteem and self worth.
I think you should get some drug support OP, so that you can tell your wife to make the choice of her family over her habit, or leave until she does.
This is what any addict/alcoholic needs to make that decision.
Best case scenario, she kicks it, and becomes a member of your family again, a new and improved drug-free one.
Or she kicks it, but is still not 'into' the family and your relationship fails anyway.
Or worst case, she chooses drugs and then you must choose to save your family.
You HAVE to get help for these children. Do it right and you'll save them, you won't lose them.
If she refuses to stop, you need to get this logged with your GP, the Health Visitor, and potentially social services. You can't hope this will go away by itself. It won't.
The last option, I suppose is do absolutely nothing and resign yourself to living like this until one or other of you flips. Meanwhile you know that you poor dc are being harmed psychologically every second this goes on.
I truly wish you all the best. This is a horrible situation, you'll need a lot of courage to tackle it. The drugs advisory people should be able to help you here.