I have been married for 20 yrs and last year was a very bad year for the both of us . Our son left home?

my wifes dad was ill in hospital our other son had brick thrown in his eye and the stress caused arguments between us which left my wife with anxiety, which she was told by the doctor to go to gym which will help her to get better At the gym i finally found out that she had met another man but she insists they aregood friends and nothing ual had gone on ....Now she wants to end the marriage because i can`t accept she has a friend at the gym although she is acting strange and almost tenager likei. Is it possible for me to carry on with the marriage knowing she has a nother bloke at the gym or do i end it like she says