I would not go with her! There absolutely nothing wrong with you expecting a nanny to stay in the house while you work. If anything they should work on a plan to reassure you that they can be trusted. As above, go with your gut x
Definitely do not go for this woman. I also find it hard to trust nanny's with my baby and will only be hiring one to spend time with my baby in the house while I work and do other things. I need to be able to see them or know they are close all the time and there is nothing wrong with that!
I used to be a nanny myself before I had my daughter. I do understand where your coming from but from a nanny point of view nannies like to take the children out to experience new things like baby classes, the park or for play dates etc. It's very beneficial for the baby and also helps the nanny by breaking up the day and being able to see other people and a have a chat, as being a nanny can be lonely just like being a mum too. If your hiring a nanny you do all the checks and you do a trial day so you can see how the baby is with them and then go from there. Expecting a nanny to stay inside all day everyday is a lot and have seen a lot of nannies leave because of it as it doesn't show trust and becomes boring as there is only so much you can do in the house. I completely understand as a mother your worried about leaving your child with someone who is basically a stranger as I would be the same. But go with your gut if she doesn't feel right then try someone else.
Your at home and can hear them most of the time so eventually allowing the nanny to go out for some of the time also shows trust on your end. It will be so beneficial for your little one rather than being cooped up at home
Go with your gut. If it doesn't feel right, pick someone else. You need to be comfortable with whoever is looking after your most prized possession.