Like the proverbial "Does this dress make me look fat?" question, there is no good straight answer to a wife's apology for bad behavior toward you.

Our BP culture holds one responsible for others’ feelingz, fears overt conflict or disagreement, and insists that everyone pretend to be friendz, so we have been conditioned to unconditionally accept any apology, however insincere, and to validate feelz around it as well. Weak, passive-aggressive, or manipulative people often use apologies as a get-out-of-jail-free strategy to avoid consequences for bad behavior. Thus, an "It's OK" or "No worries" or even "Apology accepted" may suggest that an apology afterward is a free pass to avoid consequences for bad behavior, or that you are too beta to enforce consequences. But replies like “You SHOULD be ashamed,” “Don’t let it happen again,” or “I expect more respect from you in future” just display butthurt and that you're trapped in your wife's frame, which is even more beta.

Your two good choices: Oak, or Rock

You should choose either an Oak (to give comfort without supplication or compromising your standards) or a Rock (to emphasize boundaries or expectations) response, as appropriate.

Oak responses. Oak responses providing mild comfort could be "Glad you're feeling better now," a smile and a kiss on the forehead, or "Hang in there, babe;" these give comfort for her bad feelz about her mistake ... but still reaffirm that she made a mistake and that it is hers to own. In addition, such responses show that you are (or at least are now) emotionally unaffected by her bad behavior; you're the Oak that wasn't hurt by the storm. This is perhaps a kind of fogging with which you can adjust the amount of comfort to the level you think appropriate.

If it was an out-of-character lapse on her part from typically good behavior, you’ll likely want to accept the apology and downplay the event; in this case, A&A or a funny change of subject work well. Using a recent text message example from this post, a decent reply to

I apologize for being bitchy. The kids are really bugging me. Kid 2's inability to do anything and Kid 3's attitude

might be

What's for dinner? Kid stew?

or the ever-favorite turn to sexual innuendo

“You HAVE been a bad girl, haven’t you? Remind me to spank you in bed tonight!

These are higher-comfort Oak responses.

Apology after hard no. Men here have reported apologies after hard rejections for sex. And /r/DeadBedrooms is rife with get-out-of-jail-free apologies and partners stuck forever playing the direct comfort game. To an apology after an occasional hard no from a generally responsive wife, a kiss on the forehead and “Hope you’re feeling better soon. Goodnight” is an OI Oak response that provides some comfort without absolving her of responsibility for the rejection. This can be adapted in various ways as you see fit for your current situation; for example

“Hope you’re feeling better soon. Hey, I’m too wired to sleep right now; I’m going to the gym to lift. Sleep well, babe.”

Or (only if you can pull off funny with a big smile, total OI and complete lack of sarcasm or butthurt)

“Hope you’re feeling better soon. Hey, I’m too wired to sleep right now; I’m going to the gym to lift. If you hear a loud boom echoing across town, that’s just my balls exploding.”

Of course after a year-long dead bedroom, comfort is no longer appropriate, and a Rock response such as /u/Scubastyles reports in this post is called for.

Rock responses. The best Rock reply is usually simply no reply (STFU). "OK" or "Acknowledged" or "Thanks" are weaker; STFU is best unless you deliberately choose to soften the stone a bit.

For major transgressions with necessary consequences, this is the time to enforce them, without anger or overt emotion (be an immovable Rock). For example, “I’m glad you recognize that withdrawing all of our retirement savings to buy shoes was a bad idea. Because we need to manage our money better, I am taking over the family finances.” For extreme violations such as physical attack or illegal drug use, “I will immediately divorce you if this ever happens again” must be overtly stated in response to the apology. (But never state consequences unless you are 100% committed to following through.)

Rock, or Oak?

Whether a Rock or Oak response is called for depends on your good judgement of the specific situation. If she means the apology as an affirmation and acceptance of your boundaries and leadership, an Oak response is in order (unless the infraction is too severe or repeated too frequently to comfort any more). But when it is merely a too-often-repeated get-out-of-jail-free-for-bad-behavior request, or a "shitty apology" to test how much you're willing to let slide, a hard Rock response is required. No reply to a text. In person, a silent stare for several seconds (well into uncomfortable silence, duration calibrated to the level of the infraction or test), followed by a change of subject. If she presses for a verbal response to break your frame, "Thank you for your apology," "I acknowledge your apology" (not "accept" unless get-out-of-jail-free is your deliberately chosen intent), “I’ll take that into account,” “I heard you,” or “This subject is closed” as fits your intent and WISNIFG Broken Record or leave from there. Always, always remember that “verbal intercourse is optional”. You decide your response only as you see right and appropriate; you have absolutely no obligation to accept an apology or to validate feelz when someone has wronged you, nor even to respond at all, but you may deliberately choose to do so, in whatever manner, in congruence with your values, vision, and leadership goals.

Many apologies will be a mixture of sincere and shitty (or at least some hope for a get-out-of-jail-free card), so you'll have to evaluate both the original infraction, the larger context (first time or repeated), and the sincerity in determining your Oak or Rock response.

Own your own shit

And if you are a weak beta using apologies as a get-out-of-jail-free strategy for avoiding the consequences of your own poor behavior, FFS stop it, become a man and OYS.