What do you mean when you say you don't have access to the server? You can't use SharePoint at all nor the web services it exposes?
Or do you mean you can't log on to the server directly? You wouldn't need to do that anyway, but you still will be accessing server resources.
If that's ok, then my idea is this:
- Create form and publish to form library
- Create receive data connection from child list to display data in fields you create in the form
- Create a submit data connection that submits to the parent list using the CAML method and a built-in Lists.asmx web service via this method