My son-in-law's auntie has described me as part of her family. What relationship am I to her, and her to me?

None,
Some say family by marriage. The closest term is "family by marriage" which means you have a family member, married to one of their family members.

I go with Chuck.
If you want to look at all of the relationship meanings, Google your "exact question" and you will see all of the definitions.

She wants you to be part of the family! Put technicalities aside.
I have an 'aunt' who is divorced from my father's brother and is absolutely no relation to me, but she's still my aunt, plus the mother of my cousins.
I have several Facebook 'relatives' who are related to my sister's ex husband.
Enjoy it.

I can agree with what you said but, telling us to "Put technicalities aside" Should have been "Putting" technicalities aside" is more correct. She may not want to be part of the family and was asking how to handle it, maybe? I did not read it that way though, just possibly.

I meant Put. The imperative. Put the lime in the coconut.

Where I come from I would say I am putting the lime in "de" coconut. ; )

I stopped taking orders back in 1959.

Imperative is defined as a requirement or an order. An example of imperative is a sergeant telling a soldier to do fifty push ups.

The question is simple, it doesn't require emotion. Legally there is no family relationship. Her son-in-law is family by marriage. His Aunt is his Aunt, and no relation to her, only to her son-in-law.

Relationships are defined by how well you like or dislike a person. Not unusual to "adopt" a person you have no blood ties to, and vice versa disown a blood relative. Legal definitions only apply to legal proceedings and people can make what they want of other people. Blood ties mean a lot to some, but doesn't mean squat to others.