There is something else at the root of her actions, and I believe he meant it to be jealousy.

The very first lie she urges her lover to tell (that is, to let the Queen imagine he loves her) is just the thing a jealous woman would invent to try her lover and the Queen, if she suspected the Queen of loving him, and him of being seduced from her by the worldly advantage of marrying the Queen.

And all the other lies are best explained on the supposition of jealous experiments.

At the last she is satisfied; the crowning test had been tried.

Through a sea of lying she had made herself sure of Norbert's love, and she falls into his arms.
Had Browning meant Constance to be an image of self-sacrifice, he would scarcely have written that line when Norbert, having told the truth of the matter to the Queen, looks at both women, and cries out, "You two glare, each at each, like panthers now." A woman, filled with the joy and sadness of pure self-sacrifice, would not have felt at this moment like a panther towards the woman for whom she had sacrificed herself.
Even as a study of jealousy, Constance is too subtle.