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You gotta be careful with those nukes, the up the AI Progress a lot and have almost no effect on AI homeworlds because of the level of the ships there. Nukes are better for other large planets that don't have a lot of V/Core ships on them.
The best idea with those homeworlds is generally to try to take out all of the outlying ships on them in general. Go for each guard post individually, clean it off, and then take the command station itself. If you just go straight for the command station, they'll all gang up on you and it's a lot harder. If there are ion cannons, then taking them out early can also be really good.
Also, it's a good idea to have a lot of ships of a high level, 1500 or so is okay but not stellar. You can also bring a mobile builder over to build some turrets on the AI planet, although now that you've nuked it that wouldn't work. But you could do that on the second AI homeworld. Having enough high-level bombers is really important for killing the fortress and the forcefield, and the command station itself for that matter.
Just bear in mind that when you kill that command station, the AI Progress goes up again (by 100), and any core ships remaining may make a beeline to your home station. It can be easy to lose right when you are taking out the first AI, so just be on your guard. It's uphill all the way from here, it gets harder instead of easier after you take out the first AI. So getting prepped to kill the second AI home planet, and killing them both at the same time, can also be a great tactic if you can muster the forces to do it. In the meantime, avoiding alerting the AI homeworlds to your presence when you are not in the process of attacking can help.
That's a lot of generalized advice, and really the strategy of it can vary quite a bit. You can bring in lightning missiles to help clear out groups of enemy ships, for instance. The main thing is to try to divide and conquer, just engage as few of their core ships at a time as possible, with as many of your ships as possible, and that's the best way to win. Just keep darting around and chipping away until there's nothing left, and then go in for the kill!