HTTP to HTTPS clean redirect - .htaccess

Question

I have been searching the net and this website too and following some suggestions I managed to get it limping but it's still not perfect.
Here is the problem. When someone is accessing my website using plain HTTP, it redirects them to HTTPS but the url looks like this https://www.domain.com/index.php?rewrite=1
That is ugly alright but that's not the biggest issue here. The problem is that when members of the website try to log in, after filling out the details and click sign in, the page reloads to https://www.domain.com/ blanks the log-in fields. Typing in the info again and click sign in, member can log in on this second attempt. It becomes frustrating to those that access the website with plain http until they figure out that they want to use https instead.
However I would like to fix this problem and I ask your help for it.
Here is my current .htaccess file, I know that there is something very simple to change but I can't spot it.
Thank you!
IfModule mod_rewrite.c>
Options +FollowSymLinks
RewriteEngine On
RewriteCond %{HTTP_HOST} !^www\.
RewriteRule ^(.*)$ http://www.%{HTTP_HOST}/$1 [R=301,L]
RewriteCond %{HTTP:X-Forwarded-Proto} =http
RewriteCond %{HTTP_USER_AGENT} !(SEAOSEAPP)
RewriteRule . https://%{HTTP:Host}%{REQUEST_URI} [L,R=permanent]
# Get rid of index.php
RewriteCond %{REQUEST_URI} /index\.php
RewriteRule (.*) index.php?rewrite=2 [L,QSA]
# Rewrite all directory-looking urls
RewriteCond %{REQUEST_URI} /$
RewriteRule (.*) index.php?rewrite=1 [L,QSA]
# Try to route missing files
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} public\/ [OR]
RewriteCond %{REQUEST_FILENAME} \. (jpg|gif|png|ico|flv|htm|html|php|css|js)$
RewriteRule . - [L]
# If the file doesn't exist, rewrite to index
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule ^(.*)$ index.php?rewrite=1 [L,QSA]
</IfModule>
# sends requests /index.php/path/to/module/ to "index.php"
# AcceptPathInfo On
# #todo This may not be effective in some cases
FileETag Size
<IfModule mod_deflate.c>
AddOutputFilterByType DEFLATE text/text text/html text/plain text/xml text/css application/x-javascript application/javascript
</IfModule>