Force https and non-www urls, not working in subdomain - .htaccess

Question

In the public_html folder which is the root folder of my main site thesite.com, I have this htaccess file:
RewriteEngine on
RewriteCond %{HTTP_HOST} ^m\.thesite\.com$ [NC]
RewriteCond %{HTTP_HOST} ^blog\.thesite\.com$ [NC]
RewriteRule ^ - [L]
RewriteCond %{HTTPS} !=on
RewriteRule ^ https://%{HTTP_HOST}%{REQUEST_URI} [L,R=301]
RewriteCond %{HTTP_HOST} ^www\.thesite\.com [NC]
RewriteRule ^(.*)$ https://thesite.com/$1 [L,R=301]
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule ^category/([^/\.]+)/([^/\.]+)/([^/\.]+)/?$ category\_product\_list.php?mid=$1&sid=$2&did=$3 [L]
RewriteRule ^category/([^/\.]+)/([^/\.]+)/?$ category\_product\_list.php?mid=$1&sid=$2 [L]
RewriteRule ^category/([^/\.]+)/?$ category\_product\_list.php?mid=$1 [L]
RewriteRule ^p/([^/\.]+)/([^/\.]+)/([0-9]+)/([0-9]+)/([0-9]+)/?$ product.php?id=$2&vid=$3&mid=$4 [L]
RewriteRule ^p/([^/\.]+)/([^/\.]+)/([0-9]+)/([0-9]+)/?$ product.php?id=$2&vid=$3 [L]
RewriteRule ^p/([^/\.]+)/([^/\.]+)/([0-9]+)/?$ product.php?id=$2 [L]
RewriteRule ^offer/(.*) product_offer.php?ind=$1
RewriteRule ^([^/\.]+)/?([^/\.]*)/?$ $1.php [QSA,L]
Here, am forcing non-www url as well as forcing https URL for the thesite.com. And I have two subdomains: m.thesite.com and blog.thesite.com.
Both are in separate subfolders inside public_html.
The m.thesite.com is in /public_html/m.thesite.com/ folder. And it has this htaccess file:
RewriteEngine On
RewriteCond %{HTTPS} !=on
RewriteRule ^ https://%{HTTP_HOST}%{REQUEST_URI} [L,R=301]
RewriteCond %{HTTP_HOST} ^www\.m\.thesite\.com [NC]
RewriteRule ^(.*)$ https://m.zapteka.com/$1 [L,R=301]
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule ^category/([^/\.]+)/([^/\.]+)/([^/\.]+)/?$ category\_product\_list.php?mid=$1&sid=$2&did=$3 [L]
RewriteRule ^category/([^/\.]+)/([^/\.]+)/?$ category\_product\_list.php?mid=$1&sid=$2 [L]
RewriteRule ^category/([^/\.]+)/?$ category\_product\_list.php?mid=$1 [L]
RewriteRule ^p/([^/\.]+)/([^/\.]+)/([0-9]+)/([0-9]+)/([0-9]+)/?$ product.php?id=$2&vid=$3&mid=$4 [L]
RewriteRule ^p/([^/\.]+)/([^/\.]+)/([0-9]+)/([0-9]+)/?$ product.php?id=$2&vid=$3 [L]
RewriteRule ^p/([^/\.]+)/([^/\.]+)/([0-9]+)/?$ product.php?id=$2 [L]
RewriteRule ^([^/\.]+)/?([^/\.]*)/?$ $1.php [QSA,L]
RewriteRule ^offer/(.*) product_offer.php?ind=$1
For this subdomain also, I need to force https urls as well as non-www urls.
It seems to be working for the main site. I mean thesite.com. But when I try to access the m.thesite.com, it seems to be internally redirecting to the files of thesite.com instead of the m.thesite.com. I mean the url is being shown as https://m.thesite.com/ but the pages are from https://thesite.com
I have been trying to debug the issue for several hours now. Probably it could be something small that I missed. Any ideas?
BTW, thesite.com is having Wildcard SSL installed.
EDIT
Am sorry if my explanation was confusing. When I said url is showing as https://m.thesite.com/ but the content is from https://thesite.com/, I meant to say that in browser the url is shown as https://m.thesite.com. But the template file contents where from the desktop version of the main site thesite.com. The m.thesite.com is mobile version of the site. The pages that displays the contents where separate in both the desktop and mobile version of the site.
Like you see in the htaccess code that I included above, there is some PHP files inside the /public_html/ folder for the desktop version. All the files for the mobile version of the site is in /public_html/m.thesite.com/ folder.
So, in short, when I try to access the https://m.thesite.com/, it is displaying the index.php page from /public_html/index.php instead of /public_html/m.thesite.com/
So that's how I found that there's issue in the routing.
EDIT
VirtualHost entries fetched by using this command /usr/local/apache/bin/httpd -S:
I have also checked the Apache version and saw that it's 2.2.27 using the command: httpd -V
So I tried adding this line in the htaccess file:
RewriteLog "/logs/rewrite.log"
RewriteLogLevel 9
But it was giving internal server error. So I tried this line instead also:
LogLevel mod_rewrite.c:trace8
That was also giving me internal server error when site is accessed. So I commented it out.