After getting to understand Eric more, Seraphine came up with a resolution.
She knew she said that she still wanted to stay true to herself even when she started living in the imperial palace – she wanted to pursue the career that she wanted, and she wanted to act however she wanted. Now, however, she realized that she had been naive and selfish.
To remain by Eric's side means to stand beside the Crown Prince of the empire.
It's not the same as how Seraphine stood by Skye, the Grand Archduke. Back then, she was enslaved by her love for him – then again, being in love is practically slavery in some way. If a woman caught a man's eye, she would want to hog his attention, and if she held his hands, she would want to hog his arms. She would want to be in his heart and in his mind all the time.
Her thoughts could end up that way again.