Can't add column to renamed table
I think your mixing up table names and module names in hook_update_dependencies().

First of all, you don't need hook_update_dependencies() to declare dependencies inside your own module. The updates will always be run sequentially, so that mymodule_update_7200() will always run before mymodule_update_7201().

Then, if you want to use hook_update_dependencies(), you would use it to declare inter-module depenencies like this:

function mymodule_update_dependencies(){
  $dependencies['mymodule'][7201] = array(
    'other_module' =&gt; 7203,
  );
  return $dependencies;
}


Now to your error. Can you check in the system table record for your module what the current schema version is? From the code and the error message I would suppose, that the database is already at schema 7200 (at least officially) but that somehow the renaming has not been done. Is it maybe possible that you have altered the database manually?

Edit: You are mixing up the arguments to db_add_field. It must be db_add_field('mymodule_field_mappings', 'fieldset_type', $spec);