I find a pattern that if I have a friendly conversation with my W, and particularly if I make her laugh she will almost immediately bring up the divorce or something related to it. There's lots of mind reading I can do here about the why but it would just be mind reading.
In my case if I end the conversation first she doesn't get a chance to do that (not great at this)
In terms of handling I think Raliced is right in that asking to put of D talk until after your test is perfectly reasonable
Both mid 30s, 2 young kids BD 7sep14 XW moved on long ago, now living with OM1 D paperwork in progress