Sounds like the root issue is merging two teams at seperate locations into one. That is a challange that requires more insight into the situation.
On a purely technical perspective, the standard suite of applications in use is important. I am going to assume you use Microsoft only because they have roughly 80% of the desktop market.
Public folders in Outlook may offer a shared file system alternative to emailing attachments. Put the documents in public folders instead of emailing them around. This addresses the latency issue and missing file issue.
To make this work, you first need to create a consistent documentation schema. Standard templates, standard naming convention that identifies the proper place for a document, revision flow (original - rev. draft - approval - posting). This addresses the version issue patially.
Using Word, a master document approach allows different individuals to work independently on sections of an overall document. This eases the pain on file merging, reduces overhead of moving full documents, and reduces the number of multiple copies and revisions floating about. The master document is administered by a single authority (for example, the overall manager) to maintain integrity. This addresses the version issue, and the file merging problems.
I am not proposing a MS solution if you do not currently use MS Office applications. However, it is an approach if you are a MS shop that deals with your budget and policy issues.