I would suggest that you approach her with a written list of facts, e.g.
I know that you are drinking more than is good for you.
The little children are aware that you are drinking.
The children were distressed by her drunkeness.
Keep the facts straightforward, and try not to get into opinion that she could argue with - she is likely to try to minimise the amount she drinks, partly to fool you and also possibly because she is not yet admitting to herself what the situation is.
If it is possible, can you find out about alcohol counselling serives in your area? Sometimes a google search is all that you need, or maybe someone on Mumsnet could help you to find out. Then give her the tepehone numbers of the GP, any alcohol counselling services, the number for AA (you can go online and find out about times and locations of local meetings). Show here that here is support available.
Then tell her what you intend to do, for example: I will keep the younger children with me until the weekend (to give you a break), and I want you to decide how / where you are going to get professional support. (or whatever else you feel is appropriate)
It is very likely that she will make all the promises in the world that she will stop on her own, and that she is apalled by her behaviour and that she will never have a drink again. She will probably be feeling remoresful, (and hungover) and she will probably mean every word of it. But please, do not let her off the hook until she has a concrete plan for how she will get help. It is so, so difficult to deal with an alcohol problem on your own, particualrly if you have been drinking for a long time.