Hi Rapael.
Congratulations on the tweediei spawning.
When we were at Bernds fish room, he demonstrated how he moves the nest. I don’t know if you saw this?
Basically he used a small plastic tub, maybe 5cm deep and larger than the cave itself. He sank this in the aquarium to fill it with water, lifted the cave carefully into it, and removed the whole thing still full of water to his rearing aquarium.
I have done this and found it very successful. When I see eggs in a nest,I set up a small (5lt) aquarium with lots of java moss, and some old oak leaves from the parents aquarium. When the fry have darkened and are moving around in the cave, I remove it and the fry as described above.
I find it easier to control the amount of food in this small aquarium, anything uneaten can be seen and removed easily.
I have been successful by removing the parents as Helene suggests, but I personally prefer to remove the nest.
There doesn’t appear to be a right or wrong way, just personal preference.
Hope this helps, good luck.
Russ