This is the best explanation I think. In this case, prep. 在 can't be omitted.
Updates:
In this case, you have to differentiate with the meaning, instead of grammar.
In Chinese, 一起 can mean
in the same place
at the same time or in company.
in all; altogether;
When it refers to in the same place, it has to precedebe preceded by 在. While it refers to at the same time or in company, it will be used alone without 在. For example, 我们一起去的。When it refers to in all or altogether, it's just 一起, like 一共. For example, 这些商品一起多少钱?== 这些商品一共多少钱?