When you have wronged someone, always apologize in a genuine, straightforward manner, acknowledging your fault, offering to make amends if material harm was done, doing so in a frank, straightforward manner.
When someone has wronged you, always accept a genuine, straightforward apology offered as above. But, always reject a weasel-worded fake apology and specify why. Fake apologies that do not even admit fault are worse than useless; they are additional offense. If the offender refuses to amend their error, shake the dust from your feet and simply ostracize them, make them thereafter a non-person to you, unless the offense also carries substantial material harm. Then, sue their pants off.
In family disputes, this may need a wee bit of tweaking. Between spouses, ignore everything in the second paragraph. No, seriously. 😉