I don't agree - more information is always better and if he doesn't do it the doubt will always be in the back of his mind. That would breed more unhappiness and animosity long term than to just find out now and deal with it either way. The truth always comes out sooner or later anyway.

Sounds like the marriage is already over, and he likely has a bond with his daughter that he won't be throwing away because of some test results.

You also need to think of the kid. Maybe not now, but if the ex is the biological father she deserves to know and to have a relationship there too.

OP, you deserve the truth and to be happy. Don't settle and do what you think you need to do to get there.