[annalex]

if one spouse wants an annulment, that's valid grounds for it?

That satisfies one condition of several. There must be a petition that challenges the validity of the marriage and it has to come from one of the spouses. After that is satisfied, the canon law will look into the substance matter, chiefly dealing with informed consent and ability to marry.

[1000 silverlings]

Money and connections make the old wheel spin faster though, just another indulgence