.htaccess - redirect links on page by removing folder from link

I followed this tutorial to manage subdomains for a MODx Revo 2.1.3 installation. The idea is that the htaccess file in the web root folder redirects calls for subdomain.mydomain.com to a folder in the web root directory by the same name as the subdomain, ie /home/mydomain/www/subdomain. Subdomain contains the MODx files to run the page, as well as another htaccess to point all further requests back to the root folder.

The better part of it works; I can view the homepage of the site (which means MODx is doing its part), but none of the links to the css, js, images, etc work, and it seems like the Wayfinder and getResources packages are failing to output. The links that are being used for the images+css+js are /subdomain/assets...etc; I need the links to point directly to the /assets folder. It's like the root .htaccess works to redirect the request to the subdomain folder, but the .htaccess in the folder doesn't point anything back up to the root for the remaining requests.

Here's my root folder htaccess, the 2nd part taken from the tutorial:

RewriteEngine On
RewriteBase /

# The Multiple subdomains part
#REDIRECT SUBDOMAIN TO SUBDIRECTORY OF SAME NAME
RewriteCond %{ENV:REDIRECT_SUBDOMAIN} =""
RewriteCond %{HTTP_HO开发者_运维技巧ST} ([a-z0-9][-a-z0-9]+)\.mydomain\.com\.?(:80)?$ [NC]
RewriteCond %{DOCUMENT_ROOT}/%1 -d
RewriteRule ^(.*) %1/$1 [E=SUBDOMAIN:%1,L]
RewriteRule ^ - [E=SUBDOMAIN:%{ENV:REDIRECT_SUBDOMAIN},L]

and the subdomain folder htaccess is simply:

RewriteEngine On
RewriteBase /

I know the site works; I can access it using a subdomain that hasn't been processed like the tutorial yet. So it's all there, I just need to sort out the link requests. Can anyone help?

---

Thanks to some assistance, I managed to find the solution to this issue.

# The Multiple subdomains part
#REDIRECT SUBDOMAIN TO SUBDIRECTORY OF SAME NAME
RewriteCond %{ENV:REDIRECT_SUBDOMAIN} =""
RewriteCond %{HTTP_HOST} ([a-z0-9][-a-z0-9]+)\.spitfireresources\.com\.?(:80)?$ [NC]
RewriteCond %{DOCUMENT_ROOT}/%1 -d
#RewriteCond %{REQUEST_FILENAME} !^/js
#RewriteCond %{REQUEST_FILENAME} !^/css
#RewriteCond %{REQUEST_URI} !^/assets
RewriteCond %{REQUEST_URI} !^/
RewriteRule ^(.*) %1/$1 [E=SUBDOMAIN:%1,L]
RewriteRule ^ - [E=SUBDOMAIN:%{ENV:REDIRECT_SUBDOMAIN},L]

The key line is RewriteCond %{REQUEST_URI} !^/. Once that was in place everything becomes accessible. Thanks to everyone who commented.