Welcome to the forums!
Unfortunately, the way your budgies have been introduced really wasn't the best. In order to give the budgies the time to get familiar with each other and to adjust to the change, it's recommended to place both cages close by for the first couple of weeks and to allow all 4 budgies closely supervised out of cage time together. Depending on how they behave and interact as flock, you can then see if they are fit to share the same cage or not.
For detailed information, you can check this link: https://talkbudgies.com/new-budgie-ar...o-budgies.html
You did well in separating the newbie budgies, given this bumpy start you can give both pairs the required time to settle back to normal.
Later on (a few weeks later), you can try again and this time to do the re-introduction the correct way, by observing how your two pairs interact when having out of cage time on neutral territory (away from cages).
If they continue to not get along, then they will have to be housed on separate cages permanently. It's sad that you won't be able to keep your budgies if they need to be separated, this is something that can happen when adding a new budgie to the mix.
Best of luck with everything and if you happen to rehome the newbie pair, then I hope they will go to a very good home with experienced owners who are bird lovers.