How to create a custom page template for resetting user password, which redirects to sub-site.

I need to create a custom page template for resetting user passwords (long story as to why) within a multisite environment. I'm having two problems with it:

1) The password verification email ends up redirecting users to the main site of the multisite environment, rather than where they started their request. I'm aware that the wp_lostpassword_url() function is defined in /wp-includes/general-template.php, but am not clear on what to add to my child theme functions.php file to redirect the requests to the local wp-login.php file (located in the child theme); e.g., I suspect that <?php bloginfo('url'); ?>/wp-login.php is ultimately the local reference I want.

2) All direct links to the local wp-login.php file such as ../wp-login.php?action=lostpassword resolve fine, but when the user submits information there, the results always redirect to the wp-login.php file on the main site. I'm unclear whether this can be fixed by editing the local wp-login.php file, or by adding a statement in the functions.php file of the child theme.

I also would really like to edit the wording of the default wordpress emails, that are sent out in relation to resetting user passwords. I'm tinkering with this plugin but it seems like overkill for just 2 emails, and I'm not sure yet that it will do what I need.

Can anyone help with suggested additions to my child theme's functions.php file? and/or any suggested edits to my child theme's wp-login.php file? and/or ideas on how to edit the default wordpress password reset emails?