That is true, it would have been different, but that scenario does not reflect the situation here at all. From the information we have, your new scenario is not what we might expect from the sister's side.
Sorry I am so long-winded, I find it difficult to write. This is spellchecked so much.
The assumptions here seem to leave out that the work and Christmas food and space provision is joint between the sisters: lunch at sister one's house, and tea (evening) at sister two's house. The sister's huge house suddenly has a space issue in this new scenario.
The 'not even a partner' line and the DH's family being left out does not reflect the OP's community 'everyone is welcome' vibe. The sister finds being asked a burden in this scenario, but our information is: 'My sis wasn’t bothered about that'.
This scenario has someone condescendingly putting up with their sister as a transactional matter for the kids. The polar opposite of the OP's relaxed, warm, social family.
The reality is both lovely sisters seem to assume the lunch sister had a say in the evening event guest list because it is a shared Christmas.
Feeling for a single parent of grown children is an odd word choice, implying pity of all things? The OP is not on her own at all. For a start, she has a lovely social family and an actual sister.
Mentioning the OP is single in this way provides the co-Christmas host with a credible invitation reason, risking the lunch host looking pretty shabby for not inviting the friend. Yet the sisters both seem lovely from what we know.
There are many different ways to approach Christmas, but I feel what op describes is not this.
quotes from op for context
"Food etc at both events and workload are shared between us."
"I don’t think the issue is that I didn’t ask first. My sis wasn’t bothered about that."
"Perhaps it’s a cultural thing but it’s certainly not unusual in the community I was brought up in. Never seen as 'entitled' but more an open, everyone’s welcome, social and kind thing to do. I think that’s why I’m surprised."
I personally feel we can trust the lovely real sister has reasons op would agree with. I can think of dozens of possibilities.