Hi SGaist and thank for the help.
For the code being in the constructor when it should not be, I only did it that way to have the simplest code possible to show my issue. I understand and agree with your point. I am working on an already existing application, I created this QtCreator project to isolate and replicate the issue. I do not call QWidget::show() in the constructor of my application.
I have made an important discovery while working on this issue: calling blue_widget->show() at the end of my code in my QtCreator project does fixe the problem, but doing the same in my application does not fix the issue. This is the 1st time I see a different behavior, I thought I had manage to have the same 1:1 behavior between the QtCreator project and my application.
Thanks for the help, I will keep looking.