How to position an element using jQuery UI .position method?
I think the problem is that you need to also load the UI libraries using the newer jQuery version. jQuery UI is a jQuery plugin, so it attaches to jQuery itself. Within your function $ refers to jQuery 10, while the UI plugin is loaded for Drupal's jQuery.

To fix this you have to use jQuery Multi to also load the libraries with the newer jQuery. You can use hook_jqmulti_files():

function mymodule_jqmulti_files() {
  return array(
   'path/to/file.js',
   'another/full/file/path.js',
  );
}


You'll need to specify the file paths, which you can put together using drupal_get_path() or get using drupal_get_library(). Once you do that jQuery Multi will automatically load those files in the newer jQuery context and then .position should be available to you in your function.