Hi Fernando,
I have to be honest here – you are the owner and it is your responsibility to breed responsibly, and to do what is best for your birds. You should have never allowed related birds to breed. You could have separated the birds or found one of them another home. You can’t say it happened “despite your efforts to separate them.” It’s as easy as another cage or another home or simply throwing away any eggs. Sometimes you have to make tough decisions to do right by your birds. It would have been much more humane to separate the siblings, than to allow offspring that had no chance of survival and suffered in the short life they had. This was physically draining on your hen. Allowing this to happen over and over is not responsible breeding. Cockatiels only breed once a year in the wild. In captivity, you can allow 2 clutches per year, as long as you rest the pair for 6 months in between. Of course with your pair, NO more clutches should be allowed – throw the eggs away if you won’t split the birds up. Regardless, you need to make changes to discourage any egg laying at all from her. I will post a list below.
As for breeding her with another male – this is not going to happen as long as she has her brother mate. Cockatiels only have one mate, unless something happens to it. She will not accept another male as long as her brother is in the same house. And I’m not sure her age, but if she has been allowed to have multiple clutches of eggs every year, she needs a long break from egg laying. Unless you plan to rehome the male, you need to accept that she and her brother are retired from breeding. Do not give them a nest box and throw away any eggs.
You need to do all of these things to discourage egg laying. Keep in mind that to lay eggs, she needs longer daylight, warmer weather, abundant food, and a quiet, private environment. Your goal is to reverse these conditions.
Limit her light to 8-10 hours by covering the cage early each evening
Do not give her anything to use as a nest – no bird huts or tents, no box, bowl, etc. If she decides to sit in a food bowl, remove it and replace with smaller cups.
Do not give her anything to shred such as paper or cardboard.
Rearrange the toys in the cage frequently.
Move the cage to a different place in the room. Move the cage about once a week, or whenever she shows signs of nesting – settling on the cage floor for example.
If she is let out of the cage, do not let her get in any dark cozy places and don’t give her free roam.
When you handle her, limit any petting to her head and neck – do not pet her on the body.
If there is no metal floor grate, then do not use any bedding or paper in the cage tray – leave it bare and clean it daily.
Thank you for asking Lafeber,
Brenda