Why would the Duke's dislike trump Harry's relationship with his aunt? If Harry wants her there, she should be there. His grandfather will have to tolerate her as the mother of the bride in a few months so can surely tolerate her as one of 600 guests in 2 weeks (if he is able to attend).
I'm not saying that Harry should invite her only so the Duke can practice but Sarah will be a prominent member at Eugenie's wedding, so if the Duke really has a hard time with that, this is great practice as this time she can be much easier ignored.
I didn't think about the televised aspect and don't think that aspect should matter that much. Any tensions that day will surely be visible as well, as we'll see pictures. And if the October wedding is the first, it will surely attract a lot of media attention (surely very negative in Eugenie's perspective) - while it will be drowned by other messages around the wedding of Harry & Meghan is 'the first'. So, yes, I agree with hel that Sarah being at this wedding is a kind gesture to Eugenie (not that they should invite her only for that reason but as it seems they have a relationship with each other this would be a nice bonus).