There are two primary reasons why individuals deliver apologies to others. First, they may feel sincerely sorry about the ways in which their choices have negatively affected another individual. Second, they may wish to minimize tensions that have cropped up for any number of reasons, whether or not they feel sincerely sorry about their contributions to those tensions.
Both of these motivations may ultimately inspire you to apologize to your spouse during your divorce process or to your child's other parent during a child custody negotiation. The sincerity, or lack thereof, behind your apology is personal and need not be justified. What may be important is that your willingness to apologize may help to ensure that your divorce or child custody matter is resolved in quicker and healthier ways than it would if you did not opt to apologize.
Apologize for what?
In order to help to ensure that your divorce process progresses as smoothly as possible, you may benefit from apologizing to your spouse, even if you do not totally understand why he or she implicitly or explicitly desires an apology. Sometimes, hurt feelings can derail a divorce process that might otherwise be much more amiable.
Even if you do not particularly care if your spouse's feelings are smarting, you may benefit personally from an apologetic gesture. After all, you likely have no desire to draw out a contentious divorce or to inflate the costs of a contentious process accordingly.
Saying "I'm sorry"
If you opt to apologize to your spouse, it is generally a good idea to sound sincere. This may seem like straightforward advice, but it is certainly easier said than done. Even when individuals are sincere, they sometimes sound as if they lack sincerity. And unfortunately, few things can inflame tensions more quickly than a seemingly insincere apology.
Once you decide to apologize, double-check that you are not doing so impulsively so that you will have no regrets once it is uttered. After that point, you can decide what method of delivering that apology will not only be most effective but will best suit your own personality and needs. Apologizing need not diminish your energy or self-esteem in any way.