To wish she would be the same with us?

You are paying for her professional services. You are not entitled to her private life. It's called boundaries!

Perhaps not everyone wants that though. If she’s pleasant, trustworthy and reliable and does her job well surely that’s enough?

Well she is both.
Of course we have friends of our own but as I said, we have always got on really well with previous housekeepers and they have become part of our family.

You call her your housekeeper but then refer to cleaners so I’m confused. I don’t have a cleaner but if I did I would hope to get on well with her though not to the extent of going out for meals with her. You sound rather jealous of her previous employer’s family. Don’t you have friends of your own?

yes.

Yes you are being unreasonable. And no, you're not! She's only been working for you for seven months. She doesn't really know you that well. Or maybe she's grieving for the previous lady still and has decided not to get close to another family. Maybe she wants to keep everything professional. You can't have the same relationship with her as she had with someone else. But you can have a good relationship given time.