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 https://wordpress.org/plugins/bnfw/ 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?