I’ve never had a nanny, but I did use two separate child minders who had very different attitudes. One had her house set up like a nursery and organized activities all the time, the other had much more of a family setting. The children did some activities, but at other times watched TV as that was what the childminder would have been doing with her own children. Both had their good points, both kept the children safe.
So I guess it’s about what you want from your nanny, OP. Personally, I would assume that the main function of a nanny is to look after your children so that you can do other things. From that perspective, as long as they are safe and contented, then I wouldn’t worry too much about how they were filling their time, but then I’m a fairly laid-back parent who tended to fit my children in around what I was doing, rather than primarily entertaining them.
Having lunch with people while the baby sleeps is a fairly normal thing I might have done now and then as a mother. The dynamic will be very different when the children are a little bit older, so the relationship and activities will probably change, assuming she’s still with you. I get the feeling some people here don’t view the nanny as someone in loco parentis so much as someone there to entertain and educate their children. Both are valid viewpoints, neither is wrong.
Taking the children to see her parents sounds like she is viewing your children as part of the family to me, rather than that she is pursuing her own social life at the expense of your children, as others seem to imagine. If the children are bored and hate it, I doubt she’ll go again as it wouldn’t be pleasant for any of them.
I get the professionalism and boundaries comments, but it seems to me from this thread that it’s very much down to what works for you and the nanny. If you’re happy with the care she’s giving, then whether she is able to enjoy the job is also important.
But there are a couple of things that suggest you don’t entirely trust her. You worry that she might not be able to manage two children at soft play and you think she doesn’t know how to entertain them all day when there are two of them there. Is this something you’ve discussed or are you going on something you’ve witnessed? Might you feel better with a more experienced nanny?
So from this thread, there’s no right or wrong. I personally wouldn’t worry about my children going on an hour each way trip to see (the nanny’s) relatives, so long as they were safe and enjoyed it. Hopefully you trust your nanny to keep them safe at her parents’ house and if you don’t, there’s your answer.
At two months in, it’s early days. I hope you and the nanny can find a way forward where the nanny is enjoying her job and your children are happy and safe. In the end, that’s what’s important, I think.