Change in Impression
Interrupting the very crucial meeting was an offense even as a princess. Freya has earned the position to talk in such meetings whereas Alora was just the first princess with no significant achievement or service to the kingdom.
Hence whatever she speaks has to be of some use for the situation or else she might not only lose her reputation she wouldn't be allowed to participate in these meetings again.
There are exceptions if she becomes the crown princess. However, she might always fail to have a good opinion of these ministers.
Alora appreciated James trusted her, however, she turned to Eugenie, seeking her permission. If she was being a nuisance by interrupting them, Eugenie will send her out before she offends anybody.
Eugenie never underestimated Alora and the latter was always above their expectations. She also didn't mind if Alora's plan wasn't going to say anything useful.