First Christmas in nearly two decades 'on her own'.
The scars of depression stick, it's very easy to travel down a negative path that you've been down before. It becomes consuming and in some cases wallowing. Sometimes CBT can be quite painful, and if she's carrying the kids issue around with her like a ball and chain its steadily exhausting her. Previous turns to alcohol often lead to reoccurrences, it's a negative means of control in that doing something, anything, is better than doing nothing and still feeling crap.
Do you share a line manager? And if so what are they like?
There is a way to gently address your concern, but it depends on if you can walk on egg shells well enough by talking around it.
"I'm concerned for a friend who I think is suffering quite a bit and I don't know if I should ask them how they are coping or not as it looks like they're struggling, and by the sounds of it it's effecting them in work as well"
That might be soft enough for her to encourage her to cough it up, but again, you know her, and the best intentions pave the way to hell. You have to evaluate her as a colleague and what the fallout could be as well as any knock on effect long term in work.
[On a side note, and this is not taking the pish, with the cloud over your recent Christmas party stuff with a certain other lady and the rebuffing of the interest, do you find you get on very well with the ladies in work as appears evidenced in the case above? You seem quite personally involved with your colleagues is all.]