Unable to store Model in Commerce Order Fields
When you assign element IDs to a relation field you need to pass the data in an array format.

See this related answer: In a plugin, how do I save an entry with a related entry

Key information in that answer:

&lt;input type="text" name="fields[customTextField]" value="My Text Data"&gt; 
&lt;input type="text" name="fields[customRelationField][]" value="101"&gt;


Note that in the input field name of 'customRelationField' relations field we are passing an array: fields[customRelationField][].

Also note the relation field data is a full replace. So if you ever want to add an element ID to an existing relation field that has relation already set, you need to get the existing IDs as an array and add your additional IDs when updating the field.