Deciding they should be called 'Aunty'

If they have been together for a few years then I think it's ok - I wasn't married to my ex and his nieces and nephews all called me aunty.

But you can call her whatever you want when talking about her to your children. Just use her name if that's what you want. Now that my children are older I've stopped referring to their aunts and uncles in that way and just call them by their names.

my SIL does this to me which I find beyond mean.
The married in men are referred to as uncle & she has never called me aunty, even when my now husband has (together for 8 years), she’s gone so far as to omit it when reading out Christmas cards to her children. It makes me really sad & I feel like she doesn’t want me in her family, despite her begging for support from my husband and I left right and centre.
I would really recommend reconsidering this one, if they end up married with kids she’s going to be the one that fosters a good relationship with her kids and you. I can’t say I particularly push my kids to call her and her husband aunty and uncle, why would I.

What does it really matter?

When I was growing up anyone who was friends with my parents were aunties and uncles, as well as my parents' siblings. We knew which ones were family and which were friends but it was just easier to call them Aunt Jane and Uncle John when talking about what we did at the weekend and with who. Often if honorífica weren't being used then subtle phrasing differences would still differentiate relationships - even now if I'm going to visit a family member I will say "I'm going shopping then I'm going round to our Michael's, do you want to come?" With the "our" indicating that I am going to see the family member named Michael as opposed to a friend/acquaintance of the same name ... I could say Uncle Michael but if there is mixed company where he has different titles then we will default to "our" (at least in my family anyway)

Now things are way more complicated with differing familial relationships and often for kids using aunty and uncle makes it easy for them to differentiate family from friends even if the specific title is incorrect. For example, my mum is my DDs grandma however to my cousin's children she is their great aunt, but they will refer to her as "Aunty Jane" because it's what they have heard their parents (my cousin's) refer to her as, but they will also refer to my cousin's siblings as "Aunty Sarah and "Uncle Sam" because they are the child's actual aunts and uncles.

My cousin's children don't tend to refer to me and my siblings as anything other than our first name in general conversation but if I have taken them out with DD for the day and we bump into people they know then they will often introduce us as "Aunty Mel and CousinDD" more for ease of explanation than as a willful lie because that is easier than "My dad's cousin Mel and her DD" especially as we do have a very close relationship.

Especially when children are younger it's easier for them to use one title for everyone rather than try to keep things clear in their heads - eg my mum's aunt, when we talk about her with family everyone knows that if you're talking about Aunty Mary you are talking about her, even if for some she is their aunt, others she is a great aunt, others she is a great great aunt, others she's a step-aunt, others she is a great-step aunt etc ... To keep it simple for everyone she is just "Aunty Mary".

You are not being unreasonable; she's not your children's aunt and she doesn't get to confer that status on herself.

In truth I can't remember how it was decided, but you are probably right about it being parents. Or by mutual consent or something.

It is not a tradition we carried on. When our DD was small the only people she called Aunt or Uncle were genuine aunts or uncles. Other adults she called either Mr or Mrs or just first name. We introduced ourselves to all her friends by our first name from a very young age.

It is, isn’t it? My bloke’s grandchildren call me Granny. I can’t believe OP is citing not being married as a reason when more than half the kids born now are to unmarried couples!

In my husbands culture everyone is uncle and aunty but for me growing up, once I reached my teen years I called all my relatives other than my grandparents by their name so it depends on your own upbringing, if you aren’t comfortable with it then just refer to her by her name, it’s your choice, not hers.

Sorry if I'm repeating anyone (I've only read the first couple of pages and all the OP's posts), but I didn't realise that being called "Auntie" was such an "honour".
I was taught to call quite a lot of my parents' friends "Auntie/Uncle " when I was a child, but that was more because it didn't feel polite to call an adult by their 1st name and Mrs/Mr X was a bit formal with someone you saw quite frequently.
Funnily enough, in my family it's almost more of an "honour" not to use "Auntie/Uncle", because you are seen as grownup enough to use first names.
Everyone is aware who are biological or "official" aunts or uncles.
I think I lean to letting a person decide what they want to be called (as long as it's not something ridiculous like "My second mummy" or something).

I don’t know. I don’t see it as a big deal. I’m Aunty Neutral to loads of kids I’m not related to and my kids have loads of unrelated aunties too. We’re a close bunch of friends and we’re northern so maybe it’s cultural.
When I was a kid we called our playgroup leaders Aunty Jane and Aunty Sarah too.

You’re clearly being petty just because you don’t like her. You’re making an issue out of nothing.

When I was a child I was encouraged to call quite a lot of adults who I wasn't related to Auntie or Uncle. I think it was because it wasn't considered polite for small children to call an adult by just their first name.

Most adults would be addressed as Mr. or Mrs. X. But if they were friends of the family then the Auntie or Uncle prefix was used.

Just to confuse things I did have many genuine aunts and uncles and also sone grown up cousins almost the same age as my parents. These grown up cousins had to be called Auntie or Uncle too!

It took me years to work out who I was and wasn't related to and how.

Was your dad who sadly died not also your brother’s father? How has your brother really let you down and why is his girlfriend paying the price?

YANBU OP.
if you feel uncomfortable then just call her by her name and your son will do the same.
She's not his aunt they don't even live together.

I think your brother's long term partner, who has known your dc since birth, is clearly an aunty.

Don't use this as a petty way of expressing your displeasure over other issues.

I kind of get this. My MIL’s partner appointed himself Grandpa for my child and I was really unhappy. They had not been together all that long, he had never been a father/stepfather to my DH, and I didn’t like him. My own father found it hurtful too as he felt this equated the two of them in their relationship to my child. I just made a point of always calling him by his name to my child instead of Grandpa and he did get the point eventually and stopped. While I probably wouldn’t get as wound up over ‘Aunty’ I do understand and suggest you just don’t use the term yourself. Your child will follow suit.

You don’t think they’ve supported you but you call his gf of over four years his current gf and talk as if they’re not serious about each other.