Ask them what they prefer, how you can be sensitive. Tell them that you have no idea what to do and for them to let you know if they have suggestions about how to negotiate this time. They, unfortunately, are going to teach you what they need. Do what you would normally do unless they let you know otherwise. This will probably, as stated, moment to moment for them, so it may be a case of just staying in the present. You are NOT expected to read them. That is too much for anyone to expect, unless there is an obvious display of emotion.
For me, I have my own anxiety only because that just seems to be the worst thing that could ever happen to someone. That they are making the effort to come, WOW!!. Like you said, this IS huge.
Celebrate family, hug your children, experience joy. All of this may feel terrible to them, but really, what is going to make them feel better?
Jen
C