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I have been working on a fantasy novel for the past twelve years, during which time there have been drastic changes. The most drastic being that I decided to cut out the first third of the story, as it was mainly flashbacks and backstory, and will just both mention bits and pieces into the actual story, and possibly have this as its own standalone story.

In the flashbacks/background story, the male protagonist comes from a wealthy family (who earned their wealth through magical and deceptive means, so their reputation about town is not the best). Whereas the female protagonist comes from poverty, moved to the city, and experienced much trauma while trying to survive. She has a chip on her shoulder about those who are wealthy. He was a womanizer back in the day, but when he met her, he realized she was "The One" (this is very simplistic, but this will do).

The back and forth and chemistry between them is quite powerful, but I realized it didn't really serve the story, as it's not so much about them as their child (although they are very prominent characters. And since then, the mother still has her abrasive, fiery attitude, and is quite overprotective of her son, but the father has seems to just be someone in the background. I've had trouble figuring out what it is that he does as he doesn't need to actually work.

In my mind, he is mysterious, calm, paternal, and some of the things that he has been doing behind the scenes will be revealed in the next story, but how do I incorporate these into the story?

Give him his own arc.

(I am amused that the gender here is the reverse of what's been a problem for a long time, but the advice applies to any character of any gender.)

In the 2017 Wonder Woman film, Steve Trevor is Diana's love interest, but he has his own arc. His job is to be a spy: To spy on the enemy, to find out what they're doing, to report back or stop what they're doing to help the good guys win the war. When he finds out what they are doing, he ends up stopping them, at the cost of his own life. This arc could have happened if he was not lost on Themiscyra and did not meet and fall in love with Diana.

So give your Dad his own arc. It can be as simple as self-reflection: he knows that he didn't come by his family wealth honestly, and he decides that he doesn't like it, so he needs to do something to make him feel like he has earned money/his position/his wife/his children/his household etc.

Give him a goal (whatever relationship or thing he feels he doesn't deserve) and have him working on it throughout the story. He doesn't even have to reach his goal; failure is also a result, and can tell us about the character.

Maybe instead of fleshing him out, you should remove him from the picture entirely --or mostly. He could be a) dead b) mostly dead c) presumed dead or d) just missing. That might seem like the easy way out, but it could actually work really well with your given back-story AND serve the interests of your narrative and your characters.

First, the pretext: Clearly, his past has caught up with him in some way. He could be out on some new cloak-and-dagger mission for his family, or, he could have refused the mission and been kidnapped (either by the family or their enemies). Or someone the family cheated in the past is out for revenge, and he got caught in the crossfire.

Next the story: Absentee fathers are one of the mythic archetypes, and can be powerful story engines --they can even be more vivid in their absence than in their presence. Depending on your story needs, you can decide if the father should be idolized or despised, if he's a good guy or a bad guy, if your character is Stronger Without Him or obsessed with rescuing him, etcetera. He can still show up in flashbacks, and you can still keep his mysterious secret machinations --that's actually even more plausible if he's not around --and if he's not all-dead you can easily bring him back in some form for the sequel (think Darth Vader).

If you opt for the absent option, you could make the father both idolized and despised.

The child could be immature enough, or naive enough about the father issue to alternate between idolizing: "Your are my only hope" and despising "It's your fault my life stinks". Every chafing at a restriction, especially one issuing from the mother, could put our protagonist into idol mode. If the child and mother are doing the you and me against the world thing, the father is despised.

The father could be idolized until a rare return makes him despised.

The father could have cast a love spell on the mother which backfired, leaving her aloof, and him obsessed.

The father could be near-suicidally depressed (think Richard Corey), without being consciously guilty.

Just a few trial balloons, not all mutually compatible.