I haven't found out how to get your wingmen to launch their Nova Bombs, nor is this required knowledge, as I have beaten it several times having the only Nova Bomb. I think it might slow you down or something, being so big and bulky, but that might just be the added alien skills. Anyway, here's how I do it:
Take 3 Avengers, 2 Firestorm. I've found that Firestorms are the best craft for dogfighting. I've only lost 1 Firestorm ever, and that was in the Final Mission. Anyway, only one of the Avengers needs a Nova Bomb, and you of course have to pilot it. But first, don't pay any attention to the Nova Bomb, the star, or the Doomsday Weapon. As soon as you enter the mission, put your engines on full, switch to Phase Cannons, and try to deal a decent bit of damage to each Shade in the battlefield. If you let them cloak before they have enough damage to make that little trail behind them, the MacArthur is most likely dead. Anyway, once you've got each Shade to this level of damage, have your wingmen all concentrate on one while you do another. Ironically, I alone can usually destroy 2 Shades in the time it takes all 4 of my wingmen to destroy 1. . .
Anyway, once the Shades are taken out, destroy all the Phantasms ASAP. Have your wingmen all go after one, then attack another by yourself. You should have been using Phase Cannons this whole time. With the Phantasms out of the way, the overall performance of the alien fleet will be greatly diminished. Then, have your wingment fire at will. From this point on, ignore them. If they die, oh well. The only things that matter are you, the aliens, and the MacArthur. If you have Vector Control Thrusters (which you should), of course, you will be able to easily draw the entire fleet after you. Get your engines on full, and gain some distance, but not too much that they'll go after the MacArthur. Then, whirl around, and use your Phase Cannons until they get to 2km. Then, switch to Tracking Tracer Cannons, and wreak havoc in the midst of their forces. Do not stop until every UFO is destroyed.
You should have been doing all this within a safe distance of the Alien Base in the area. Then, tell your wingmen to ignore the base. Now, switch to Fusion Missiles (I like having twin Sidewinders, a Permeator, and a Fusion on this mission) and get your engines to full. Fly right towards the base, and press Z when you are within 1km of it. At the same time, launch both Fusion Missiles at it. This will draw the base's fire towards you, as well as prevent the missiles from being outrun by you, and then running into you, which has happened to me on several memoriable occasions. If the base is still standing, use your Phase Cannons, they work remarkably well here.
Once the base is gone, you'll have a clear shot at the star. Tell your wingmen to retreat, then launch the Nova Bomb. Start running back to the MacArthur, because you'll have to be within 1km of it to retreat yourself. Wait by it, watching the Nova Bomb go. When it reaches full velocity, you have one minute to get your arse outta there. If you want to wait a while, though, make sure to leave at least 10 seconds for engage the Hyperdrive and the what-not.
I've used this strategy over 5 times on the bottom three difficulty modes. I only lost a pilot the first time, because I had no idea what I was doing