Hi Helenmarge,
We went through this exact thing and it took some trial and error for DS to be comfortable in his bed and new room. I think it's a combination of their development, especially mental dev't that involves imagination at this age, along with verbal and physical growth. The half years and year mark usually cause some sleep disturbance. Of course the life changes can affect it, too.
Here's what we did at first:
-made wind down longer to bed, so an extra 10 or more mins of cuddling and reading
-used a lovey and asked DS to hug it when he woke in the middle of the night and everything will be all right, and used lovely during wind down, and any other time for comfort to create a healthy attachment
-talked about how mom and dad are right here in the next room
Then we had to try:
-using a night light (I thought it would backfire bc he would see shadows but it worked for him and a couple of my friends' toddlers as well)
-opening the door and said we'll leave this open so it'll be alright (this worked the best)
The worst nights we would have to lay down next to him, especially if he got emotional about daddy being gone. The next night, we go back to our usual routine, until he starts to get hysterical. Then we say, we'll stay for a little bit then daddy is going to leave the door open for you and go downstairs. Sometimes we literally have to pee so we say that we have to use the bathroom, night night, and leave the door open for him. We make a big deal about the door and it's helped him.
Some members here have tried discussing the day with their toddlers so they can process it and let it go...
For your situation, I would start and end by talking about anything happy that happened that day, colorful things like tickling, the playground, dessert, friends, etc... before reading, then choose a low key, calming book, perhaps one with a song. if all this doesn't help and she continues to talk about spiders, she might have to help confronting the fear... In this case, I would frame the topic to make it positive... spiders tickle when they crawl, they spin beautiful webs, they live with other bug friends in the grass, etc... Or find a book that has a friendly spider.
Hope this helps! Let us know what you think.