Forgot name pls help

I forgot the name of this bug I really wanted to read the fourth volume. So it is bl and there is a good plot but its also very smut.
This guy goes out to a rural countryside type place and there is another teacher there and he has a wedding ring on maybe or maybe a tan from a ring. The whole time we think hes cheating but i think volume/ ch 3 ends off with him cryinv and confirming that his husband left him for a woman and they had a child