It sounds like either something wasn’t explained properly to your relative or else it was misunderstood. I have never heard of a policy whereby the anullment cannot proceed because of papers not being filled out by a partner’s parents.
In any case, you will not encounter such a situation. Such an unequivocal demand is not part of the anullment process.
When you file for an anullment you will name “witnesses”-- optimally, people who knew you and your spouse before (or at the beginning of) your marriage. An anullent, in essence, states that either you or your husband, or both of you, did not have the ability to enter into a Catholic marriage at the time you were wed. These witnesses hopefully can support this claim and must do so in writing. BUT- the person filing for the anullment decides whom they would like to ask to be witness. The witness is under no obligation to cooperate, but does this usually to help out. There is no mandate on who may or may not be a witness-- except, of course, that they would have to have known both of you during the time in question. The church never demands that any specific person must give witness or testimony of any kind. Naturally, the person who files will have to fill out paperwork. I named four witnesses in my anullment; my sister, my cousin, a friend and my ex-husband’s cousin. My sister filled out the paper work right away. No one else did it for a long time and the church wanted to have more testimony than just me and my sister. After a while my friend sent in testimony and the anullment was granted. So only three people actually filled out papers: me, my sister and my friend. I do believe they prefer more than just two witnesses.
If you know a priest with whom you are comfortable please do discuss this with him. I would like to see your mind set at ease.
Pax et bonum