Kovu may have wanted to ask Simba to marry Kiara. Had Zira not attacked Simba when Simba was meeting with Kouv, nobody in the Pridelands would have any direct evidence that Kovu was still working for Zira. However, the lyrics in "One of Us", particular "for we know he would do what he's done" indicates that everyone pretty much EXPECTED him to turn traitor.
Now, Kovu may have felt that he kind of brought it upon himself when he did get in trouble after Zira's ambush and he got found out (even if he hadn't been in on the ambush). However, if Kovu had not been found out but had asked Simba to marry Kiara, the kingdom, including Zazu, may have talked him out of it, if Simba would even have considered it. Simba's rejection would now make him feel that Simba was an obstacle to him getting Kiara. Hence, now he WOULD have a motive to kill Simba again( his previous ones had been lost when he found out the truth about Scar): to marry his daughter.
Zira picked a very bad time to ambush. Had she not ambushed at all, or had she done it earlier before Simba found out the truth about Scar, things may have turned out in Zira's favor.
At least, that's my view. Also, recall how Kiara defied Simba and went to go find Kovu even after his exile? Had Simba told Kovu no about marrying Kiara, Kiara may have gotten angry enough to offer to run away with him. (In the actual timeline, Kovu, after his exile, suggested that they do just that.)
Kovu still would have been upset about being lied to about Scar, but Nuka's death wouldn't have happened and there wouldn't have been the falling out with Zira over it. Thus, Kovu either would have ran away to form his own pride or taken Kiara with him to the Outlands. Either way, I think he'd have kept in contact with Zira. Zira would have picked up that Kiara had run away and perhaps used it to either sneak up on Kiara and hold her hostage to lure Simba into some kind of confrontation or she'd have assassins ready to attack a part of the search party for Kiara that had Simba in it.
Also, they might even be able to catch Simba by himself, looking for Kiara (if Mufasa went alone to the Elephant Graveyard to rescue Simba and Nala, it's not beyond the realm of possibility to think that Simba may have gone off into a part of the Outlands, by himself, to look for his daughter.)
On the other hand, if Simba DID let Kovu marry Kiara, that would make Kovu the Next In Line for the Kingship of Pride Rock, which means that now, instead of a bloody battle, all Zira now would need to do is find a way to kill Simba and the throne would be hers by default. (Of course, Kovu could well have double-crossed her and tried to stop her from killing Simba. As, unlike in the actual timeline, she didn't see Kovu betray her, she would probably think the whole marriage thing was a scheme to take the throne and take over.)