1) We moved because our house was too small.
BECAUSE is a subordinator. This is a complex sentence.
2) A tree surgeon removed the branches that were dead.
THAT is a relative pronoun. This is a complex sentence.
3) This is a book the children enjoyed.
My guess is that the this is a complex sentence which is missing a relative pronoun.
THIS IS A BOOK THAT THE CHILDREN ENJOYED.
THIS IS A BOOK WHICH THE CHILDREN ENJOYED.