Hi Lavad,
Welcome to MB!
how likely is it that an affair given the time it exists has any sustainability in the long run?
Most marriages based on A's will NOT last. Eventually, one or both partners will finally realize that if they cheated on their former spouse, that they're likely to cheat again. Also, the same 'issues' that caused them to stray in their first M will almost surely pop up in the second M.
How can I make her account for the time at work so that I know she is not leaving the premises to meet him?
You Can't. Period...
Are their emotions that high during an affair that they cannot even realize how complex their situation is with work, a dying woman and 4 year old child?
They are both overcome with 'emotions' and 'In-Love' FEELINGS. They are NOT thinking. Don't expect them to have ANY clear thoughts while they are addicted to each other.
My best advice to you is to read up on all of the articles here on the MB site, then expose the A to everyone that you can think of that will assist in breaking up the A.
Your W or the OM must quit their job and they must have 100% No Contact (NC) for the rest of their lives. Any contact, no matter how slight, by phone, text mssg, e-mail, will set you back to square one.
Once NC is in place and the A is exposed, there will be a period of withdrawal. An A is an addiction much like a drug addiction. It will take some time for your W to withdraw from the OM.
It is possible to rebuild your M... but the first step is to end the A and establish NC...
Semper Fi,
RIF