Hi @HomeEduDilemma
I can understand your quandary. I'm surprised at how many voters have suggested you are being unreasonable - I don't.
That said, your question is of necessity provocative. I don't think you are really suggesting HE for your daughter JUST because she says she wants it. It sounds as if YOU can see plenty of possible benefits too, but it feels hard because she is doing well in school, you chose it for your DS as he wasn't, and your husband isn't keen on the idea.
I have a son who I (for the last 2 years) HE and a daughter who goes to school. They are both older though - early to mid teens. But it has been really important in our family to make sure the needs and wishes of both children are listened to and responded to as best we can.
Tbh I think your issue similar to other questions about how we balance needs/wants/ strive for fairness within a family more generally - it's not just about HE.
My belief is that as parents we should strive to meet the needs of all our children as equally as we can. As well as recognising the needs and wants parents. All children should be equally valued, and their needs and wishes should be given equal precedence as far as they can be. Of course, this is not always easy! And children can be fickle, and not necessarily know what they need vs what they want. Adults too!
At 6, and at the the end of the summer holidays, it is not too surprising that your daughter says she wants to be HE. So maybe some more time is needed for her and you and your husband to think and keep things under review for a few weeks. But if her feelings stay the same for some time I really think it is important to take these wishes seriously.
Regardless of what an outsider might observe about her education, insisting that she keeps going to school when her brother is home educated seems a recipe for embedding feelings of resentment, possibly a sense of rejection, and a sense that she is less important than her brother is. This is likely to have long lasting negative impacts on her life, much more than any academic achievement. Perhaps that argument might be helpful to discuss with your husband?
Both you and your husband's views, and your own day to day happiness (you will be doing the bulk of the HE I think?) are important.
I think you are absolutely right to be be thinking seriously about this - listening to your daughters wishes, and really thinking about her emotional needs. There is no need to leap into a decision, and clearly it is really important that your husband is happy enough with the decision you and he make for the family. As others have said, HE groups (e.g. on FB) might be useful to help explore what HE for your two children together might look like, and how easy (or otherwise) it might be for you to meet their needs together at home.
Good luck!