If she's on the net, email is another way of keeping close and frequent contact, in a way that sometimes might be less stressful than phoning. People can write an email in the small hours when they can't sleep and they want to say things, and feel they can't phone, and so forth.

Going back to work soon might be a good idea. Colleagues can sometimes be very helpful.

The whole business burial or cremation and so forth can have the side effect of keeping the bereaved person pretty busy at a time when that's actually what they need.

Can't give advice, of course, but whatever she says about not needing you to come at this time you might perhaps decide not to take it at face value. Six hundred miles is a long way, but your first message said she wanted you to come if you could.