Ok, that’s what I expected.
I’m not to for sure though, whether this thing will work on your case. I did play with htacess as well, when I’m trying to achieve subsites capability with MODx with one installation.
It seems to me that all the external files can’t be access by your browser, due to this uncommon setup for your htaccess system. I’m assuming when they create this so called alternate domain, they didn’t expect that alternate domain to be used on a virtual directory that are handled by another mod_rewrite, which is in this case, it will be MODx mod_rewrite that does the redirecting to the index.php, and index php responsible in translating the virtual directory.
Is it possible for you to host the domain as regular domain, but let it directed to the root install of your MODx? You can use my core hack, to enable several domain being hosted on one modx installation. This one of the solution that I can offer to you. All MODx functionality will works just fine, so far I haven’t encounter any problem yet.
Another solution would be to let the browser search for the files using absolute address. But you told me that the <base href="" /> does not work. I’m assuming you use your
http://www.fazalkhan.co.uk/ domain in it, not the cromwellcare.com, but it’s still doesn’t work.
So one other solution will be to try creating the real subfolder on your too folder with your domain name, and copy all necessary file for your template. I know this solution might be cause the front page to be directed to the subdomain file listing or whatever startup file that this thing going to fo. But I’m assuming that the request all being made relative to this subfolder, so if we are able to allow the real files located to where it’s suppose to be in alternate domain, then it’s sppose to work.
Hope this can help you troubleshoot the problem.
It’s just my several cents

(Trying to make a joke here

)