I only read a few posts... and skipped to the end...
But this is my idea of the situation... when two people are in disagreement or fighting, and you interfere... they will tend to join forces and team up against you. For all you know, your mother and father could be having a 'cold war' and for you to sound the alarm, you may bring their frustrations and wrath on yourself.
So you have to look to see what is there to gain from this?
If you tell you father:
(a) and he doesn't know - he will be forced to confront her to save face and this could lead to divorce.
(b) and he does now - he may either confront her openly - leading to divorce OR try to silence you and add more to your restless consience.
If you tell your mother:
(a) and she knows you father doesn't know - she may try to silence you OR be guilted to tell your father - which could lead to divorce
(b) and she knows your father knows - she may try to silence you so that things can go back to 'normal' OR she may feel she needs to be open about this, and may unwittingly force him to have to take action and divorce her.
If they divorce, then life as you know it will be in turmoil for however long it takes for both parents to recover.
- your interference in their relationship may be tied to being a major factor in their divorce... and your relationship with your mother may be strained to a breaking point... possibly even with your father.
So you risk a lot of damage to life as you know it by being confrontational. Yes, cheating is wrong... but it's up to the cheater to confess --- not for you to force a confession out of them or to confess for them. If you father chooses to ignore her infidelity, then that's his right --- as foolish as it may seem.
There is also the possiblity that there is nothing wrong with your parents' relationships... perhaps they've embraced a form of 'openness' or have some silent agreement (aka. one cheated and now the other is allowed to... or... your father has become impotent).
Also, if you approach your mother with this information... then you'll have to suffer the consequences of violating her privacy... along with how she'll react to your accusations.
The only outcomes possible from your interference is divorce, hard feelings between you and your mother (and possibly father), or humiliation for making assumptions (it wasn't cheating but something else... etc.).
So it's up to you to make the assessment and decide which outcome you favor more... or just let it go.
"The weakest soul, knowing its own weakness, and believing this truth that strength can only be developed by effort and practice, will, thus believing, at once begin to exert itself, and, adding effort to effort, patience to patience, and strength to strength, will never cease to develop, and will at last grow divinely strong."
- James Allen