Hi there and
to the forums!
We'd love to see photos of your budgies if you have any to share!
It can definitely be difficult to see them flying around in chaos while still wanting them to stretch their wings! It's going to have to be a bit of a learning curve for them - they'll have to figure out their surroundings even if the first few times it seems like they're in chaos! To make the room safer for them, be sure to cover all windows and mirrors, remove breakable or easily tipped items, and any toxic plants, chemicals, etc. Additionally, try and stop up the space behind bookcases, sofas, etc. Doing so will remove a lot of stressors from their environment. You should also close any doors and curtains to sort of provide to them an enclosed space.
Then, you just have to go for it! Since it sounds like they will come out of their cage if you open it, try and make it less stressful for them - you can attach perches to the outside of their cage so that they have a familiar place to rest, and you can put a little millet nearby to entice them a little bit. You should stay in the room and supervise them, and reassure them and talk to them. You can also put on soft music, as silence to budgies signal danger and may stress them more.
You should try and let them out of the cage a few times a week at first, each time doing this, until they have sorted out their surroundings and are fully comfortable getting around in the room, then you can let them out daily (under supervision).
I hope that helps!
Also, be sure to have a look around the forums and read through the articles and "stickies" in order to stay updated on the best of budgie care practices!
If you have any questions after doing so, please be sure to ask as we'd love to help.