IIS websites in subdirectory => HTML source requests to root "/" points to default website instead of subdirectory

Our IIS hosts our own website. But recently we have been tasked with hosting a third party website built using Laravel in a subdirectory.

The website is loading, but most of the resources like CSS and JS files are not being loaded (404) because of the way the third-party site requests it's resources. E.g:

<script source="/js/site.js"></script>

/js/site.js translates to https://defaultwebsite/js/site.js which doesn't exist. I need /js/site.js to translates to https://defaultwebsite/laravel/public/js/site.js.

Is this possible in IIS 10?

Here's a sketch of the directory tree:

+ defaultwebsite
| + laravel
| | + public
| | | + js
| | | | - site.js
| | | - index.php
| + js
| | - ourownjs.js
| - index.php

We have two rewrite rules set up to handle redirecting https://defaultwebsite/lavarel to https://defaultwebsite/laravel/public like this:

<system.webServer>
    <rewrite>
        <rules>
            <rule name="Imported Rule 1-1" stopProcessing="true">
                <match url="^" ignoreCase="false" />
                <conditions logicalGrouping="MatchAll">
                    <add input="{HTTP_AUTHORIZATION}" ignoreCase="false" />
                    <add input="{REQUEST_FILENAME}" matchType="IsDirectory" ignoreCase="false" negate="true" />
                    <add input="{URL}" pattern="(.+)/$" ignoreCase="false" />
                </conditions>
                <action type="Redirect" url="{C:1}" redirectType="Permanent" />
            </rule>
            <rule name="Imported Rule 2-1" stopProcessing="true">
                <match url="^" ignoreCase="false" />
                <conditions logicalGrouping="MatchAll">
                    <add input="{REQUEST_FILENAME}" matchType="IsDirectory" ignoreCase="false" negate="true" />
                    <add input="{REQUEST_FILENAME}" matchType="IsFile" ignoreCase="false" negate="true" />
                </conditions>
                <action type="Rewrite" url="index.php" />
            </rule>
        </rules>
    </rewrite>
</system.webServer>

UPDATE I recently added this rule to root (default web site), but it doesn't seem to hit this rule when the laravel site requests resources. Even though I can see the HTTP_REFERER pattern is correct.

    <rewrite>
        <rewriteMaps>
            <rewriteMap name="Root" />
        </rewriteMaps>
        <rules>
            <rule name="Rewrite Root => Laravel" stopProcessing="true">
                <match url="(img|js|css)?(.*)" />
                <conditions>
                    <add input="{HTTP_REFERER}" pattern="^https://www.defaultsite.be/laravel(.*)" />
                </conditions>
                <action type="Rewrite" url="laravel/public/{R:1}{R:2}" appendQueryString="true" logRewrittenUrl="true" />
            </rule>
        </rules>
    </rewrite>

Well, I don't fully understand it myself. IIS will never be my friend :)

It started working when I change the rule to redirect instead of rewrite:

<rules>
    <rule name="Rewrite Root => Laravel" stopProcessing="true">
        <match url="(img|js|css)?(.*)" />
        <conditions>
            <add input="{HTTP_REFERER}" pattern="laravel/.*" />
            <!-- <add input="laravel\public\{R:1}{R:2}" matchType="IsFile" /> -->
            
        </conditions>
        <action type="Redirect" url="/laravel/{R:0}" appendQueryString="true" logRewrittenUrl="false" redirectType="Permanent" />
    </rule>
</rules>