If a child is used to being with or near its mother 24/7, IMO it will panic and get stressed if the mother leaves it for any length of time. This would only be natural - like any baby animal calling for its mother to let her know where it is if it is lost. I don't think they are being manipulative (let's not get into a Gina Ford debate!), it's just instinctive.
I left my dd for an hour or two a couple of times when she was a few months old. I think she would have been ok with my sister because my sister held her from the beginning but I had to leave her with my Dad. Maybe it was because he was a man or wasn't that sure what to do with her but she cried non-stop the whole time I wasn't there, until she was shaking and hyperventilating. It was quite scary when I returned. It took a while to calm her down and she was looking up at me in a panic and patting my face to make sure it was me.
Another time, once she could crawl, she was trying to climb up the stairs for the first time because she assumed I was up there. I'm sure other people have had similar experiences.
Based on this, I would say there is no doubt that some babies can become very distressed when they are separated from their parents, particularly in the first few months. It must do them some harm at the time but, whether there is any long term damage caused, I'm not sure, possibly not? I suppose it is an argument to introduce various people to your child early on so that you have people to call on if you need a break. Some of us are not as lucky as others in this respect.
My dd also, like most little children, got upset when she first went to nursery. She was not happy! One of the nursery people took charge of her and dd spent the first few weeks attached to that person, rarely left her side or her lap! It's just natural and then they adapt and become more sociable.
When you go back to work, you will introduce your baby to the childcare people you have chosen and spend some time there together before you start work. A skiing holiday is difficult but you can still try to spend the first morning of the holiday at the childcare place with your baby and maybe she will pick up from you that the people are safe for her to be with?
We are always told that some stress in life is necessary and a good thing. As someone else has said, your dd will at least learn from it that, even though you went away, you always come back.