I do not know the name of this movie, it is somewhere in the time line of 1940's and the 1960's. It is about a husband and an acoholic wife. He does not want to leave her so he takes a mistress that lasts for years. After some time one of the children discovers the affair, towards the end of the movie the husband and the wife are killed in a car accident and the children end up with the mistress.

Could it be "Strangers when we meet"... 1960.. kirk douglass ?

I believe you are thinking of the movie Back Street, of which there are three versions, from 1932, 1941, and 1961. The basic story is that some guy meets some woman, but he's engaged, but they have a fling anyway, and then he's willing to run off with her, but due to unexpected events, their rendezvous is disrupted and he leaves town thinking she's blown him off. So he gets married and works for his father-in-law, and years later he meets his crush-girl again, and they resume the affair. Apparently, each movie ends a bit differently. The 1961 version with Susan Hayworth and Vera Miles concludes thusly:

"The situation has become untenable and Saxon decides that the only way to end the pain he has caused Rae is to kill his wife. He chooses a car accident, and of course we understand that the risk will be just a great for him. The wife dies, and Saxon survives – but only long enough to phone Rae and tell her he loves her." And then it seems that she takes in his kids.