Well she has a good friend in you.
My mum is an alcoholic and has been for about 12 years. I could tell you a hundred stories and examples of alcoholism and the effects on the alcoholic, the family,and the children.
But, I'll keep it short.
Just as people are different as individuals, alcoholics are different, and will react in different ways.
If I was in your shoes I would take the child/children if I thought she was in no fit state to look after them - alcohol or none, as it has only been a week into a break up and ANYONE would need a break from the kids at this time to 'sort their head out / grieve etc'.
However, alcoholics ARE selfish, irrational and cannot control their alcohol intake. They quite often need to be given a 'shake' as it were in to reality and realise they have responsilities and their actions have consequences - whether they think they do or not.
I would not offer to look after the children after two weeks. That imo, is time enough for self pity and self indulgent behaviour. Children come first, mum is second.
Give your support. Speak to her every day. Be there if she needs you. But you cannot mother a mother. She has to stand up to her role as a mother and lead by example.
You cannot do her job as a mother, nor will her children want you too.She has lost a partner she could replace, the children are now from a broken family which is not replaceable imo.
Support her but don't support her drinking. (sorry very harsh sounding I know)