Ladies with Rings

[Searcher]

So am I correct understanding that rings go with marriage and betrothal, but can also be seen as independent symbols of love? Or must they always accompany an official union?

As much as I understand, no, it can't be an independent symbol of love. From You are not allowed to view links. Register or Login to view. (I couldn't discern some words, excuse me, but I think the main sense is preserved):

"Ponsus (positus?) sponsa anulo debet sponse anulis...
...anulus sponse a sponso et eam datur in signum mutue dilectionis et fidei ...XXX.9.V femme ... ideo anulus a sponso sponse in quarto digito inseritur, ut sunt vena ab illo digito cordi conjungitur, sit eorum corda per sacrum matrimonii conjungentur XXX.9.V. femme..."
Thus, the approximate translation: The ring is given by a bridegroom to a bride as a sign of their mutual love and faith...Therefore the ring on the fourth finger of a bride by a bridegroom is inserted, as it is joined to the vein of the heart, let their hearts be joined by means of the sacred marriage...

Another ring, though not a lady, is found in Van Eyck's famous You are not allowed to view links. Register or Login to view.. I had always learned that ring indicated the anonymous man's occupation as a jeweler, though apparently this view has recently changed in favor of a betrothal. It was finished in 1430. Similarly, a ring is held by Jan de Leeuw in another portrait by Van Eyck; in this case, the ring supposedly does symbolize his occupation as a goldsmith. However, given the sitter's seductive gaze towards the viewer, I think here too a portrait for his betrothed is more likely.

From Wikipedia:

Erwin Panofsky's analysis in the mid century – or that the painting was commissioned as a betrothal portrait to mark a proposal of marriage intended for an unseen bride and her family.This latter theory is supported by the panel's near miniature dimensions; such a small size would have been easily packed and transported to the intended's family.
...
Yet it is interesting to consider such an idealised portrait in the context of a betrothal portrait, where the intended bride's family most likely had not met the man and are dependent solely on the portrait for an indication of his means and character. Carol Richardson observes that the unidealised representation would have been a significant novelty and shock at the time, and that, complete with the evident skill of the painter, the verisimilitude would have given the sitter weight and creditability

I have the same impression. They've often sent their portraits to an bethrothed, maybe, some were pretty original to make a marriage proposal in the same time.