Did Will forget who killed his father?

They were in the middle of a sword fight when Will proposed to Elizabeth. He has Barbossa marry them on the spot as it appears that it will be the only chance they'll get to be married. Whether or not Barbossa is responsible for Will's father's death, or whether or not Will remembers this fact never enters into the decision.

You're correct, but notice a few nuances here:

1. Barbossa had already died for his sins relating to Cortez' treasure.

Bootstrap Bill's death was related to Cortez' treasure, since Bill sent one of the coins to Will so that he could ensure that the pirates stay cursed forever.
Bill did this out of a sense of guilt for being part of the mutiny against Jack.

Will is an archetypical good guy, and he could consider Barbossa's death as the conclusion to his quest of avenging his father. Good guys tend to not hold grudges after the guilty party has died/atoned.

2. Barbossa was resurrected for a reason.

First and foremost, to bring Jack Sparrow back from the locker.
We later find out that his deal with Calypso entailed more than just Jack (also freeing Calypso), but that's irrelevant for this answer.

Will and Jack hadn't been on good terms lately. The last time he saw Jack, Jack was kissing Elizabeth, and Will carried that grudge for a long while (he talked to Elizabeth about it some time after Jack's rescue).
Notice how Will is notably quiet in the final scene of DMC (Tia Dalma's shack, a toast to Jack). Will doesn't like Jack anymore but knows to not talk about it to the others.

Will is clearly capable of setting aside personal opinion in the face of objectivity. They needed Jack back, regardless of whether Will likes Jack or not.
The same can be true for Barbossa. Will can hate Barbossa for killing his father, while also understanding that Barbossa has a role to play in the current events.

3. Bootstrap Bill was alive, in a way...

Will had already met his father aboard the Flying Dutchman. While Bill of course isn't fully alive, having seen and interacted with his father is a good enough reason for Will no longer actively seeking to avenge his father's death.

Notice how Will speaks to Bill. He makes future promises (about freeing Bill). Will's interaction with Bill was not a matter of getting to say goodbye (which was the case for Elizabeth and her father), but rather the beginning of an ongoing relationship between him and his father.

4. The pirates needed to unite.

The pirates of the Brethren Court were shown to be divided. In the end, they chose to unite and ignore petty squabbles in the face of a common evil: Davy Jones and Lord Beckett.

The scene in which Will asks Barbossa to marry him is built on the foundation of that unity, in the midst of combat with the common evil, so it makes sense for Will to not be driven by his personal agenda.

5. Beggars can't be choosers.

Will married Elizabeth on the spot, specifically because either of them could die at any point in the near future, maybe if only minutes away (which ends up happening to Will).

Will didn't really have time to shop around for a better marriage officiant. He was focused on marrying Elizabeth, and didn't care who the officiant was.

IMO Pirates of the Caribbean is set up to be a long-term redemption story for Jack Sparrow, which was more emphasized in the events of Dead Man's Chest and At World's End, and is now furthered with the next films beginning to dig further and further into Jack's past (Angelica, Salazar), while also advancing forward and beginning to fix past indiscretions (Will & Elizabeth).

"Stab the Heart, Don't Stab the Heart!" - Captain Jack Sparrow

• Davy Jones Locker (Ship Out of Water/Multiple Jacks) = Jack fears being stuck with himself, because then he has to consider the consequences of his actions. Jack is an escapist character.

Barbossa then also parallels Jack in being an anti-hero with a redemption arc, in that he's a long-term character that is mostly being turned into a better person via the connection to Will & Elizabeth (and their son) through knowing Jack. His sacrifice in the fifth film helps to solidify this idea.

Therefor, for the sake of that trope or kind of story, Will, a "heroic" protagonist, would not confront Barbossa, because it would not suit the story (I think the idea is that the ship has sailed and ultimately they need Barbossa's help)--and despite that Barbossa is responsible for his death, it was Davy Jones abuse and Jack's abandonment that Will has a beef with.