あまり can be used when you're talking about too much of a bad thing or warning about excess.
あの本はあまりにも面白かったので、読むのに夢中になっていたら、いつの間にか夜が明けていた。That book was far too interesting and while I was so engrossed in reading, the day began to break at some point.
あの本は面白かったあまり、読むのに夢中になっていたら、いつの間にか夜が明けていた。 にも can be dropped without changing the meaning.
母は、私のことを心配するあまり、体調を崩したようです。 Mother worried about me so much that it affected her health.
母は、私のことをあまりにも心配して、体調を崩したようです。Mother worried too much about me and get sick.
Changing it to TE-form made the sentence sound like a one-time occurrence.
その犬が死んだ時、先生は悲しみのあまり、しばらく仕事を休んでいました。 When his dog died, the teacher was so grief stricken that he took a few days off of work. NOUNのあまり indicates an extreme degree. に can be dropped after the あまり.
その犬が死んだ時、先生はあまりにも悲しみだと、しばらく仕事を休んでいました。When his dog died, if his grief was too great the teacher took a few days off of work. This pattern needs と after the noun and doesn't really work here. 先生はあまりにも悲しみだと、 その犬が死んだ時、しばらく仕事を休んだほうがいいでしょう。If the teacher's grief is to great, after his dog dies he should probably take some time off of work.
あまり can be used with に, but it doesn't seem to go with は.