We all know that a comma goes before a coordinate conjunction -- and, but, or, nor -- when there is an independent subject and verb after the conjunction.
...I went with her, but I did not have the chance to speak with him.
...She stopped at 1:00, and she saw that she was the only one working.
Look at this sentence:
...My mother, Margaret, left on August 8, a Monday, around 8:45 A.M., but her oldest brother, Sam, followed her and at 11:00 found her wandering near the downtown area.
With other marks of punctuation near the comma before the conjunction that tend to "hide" that comma, a stronger mark of punctuation is needed before the conjunction. The comma needs to be changed to a semicolon. The division between the two sentences has to be clear and obvious.
...She called on Monday, Tuesday, and Thursday; but Dr. Ray, who was in charge of the case, was not available.
The comma just doesn't do enough to separate the two sentences.
Happy punctuating!
Margie