You say you're clicking in front of her and nothing happens. Are you trying when the blade of light is there or when its not? The blade actually disappears for a short time after each aether filling cycle. Is there any chance you're trying before it appears, then get sidetracked by the mobs and don't see it reappear?
This is the start of the fight.
https://youtu.be/-WOxuQbHCh4?t=344
If you look in front of alisaie, the blade doesn't appear until time 6:09, about 20 seconds into the fight. They get pulled away by mobs for about a minute then finish filling it with aether at 7:17 and the sword disappears. The angle is bad but the blade reappears at 8:11, between Urianger and Alisaie, and at 8:37 they fill it some more and it disappears.
One thing you'll notice the player doing is rotating the camera to see it from the side and cycling through targets to select the sword. I don't play with a controller but you can use tab to cycle through targets on a keyboard; maybe that will help you select it if a mouse click is having trouble?
If it never appears at all, or does and won't let you interact then its a game bug you should report. You can try to reinstall the game but I don't think the issue is on your system, its more likely to be in the duty code on the server.
Good luck, I hope you get it to work.