Hi Gavsta
What they are offering is essentially a copy of your website on a micro-site within their own framework.
If you are happy with them doing this because you feel it will help generate more business for you then, by all means, go ahead. They must, however, Noindex the entire micro-site so that it does not appear in Google. If they allow it to rank then it will completely destroy all of your SEO efforts and your rankings will plummet. Google does not handle duplicate content well - it would simply not know which version to rank so would end up raking neither.
I suffered a huge penguin penalty in 2012 for trying to rank micro-sites which pre 2012 worked very well - don't fall into that trap. If they say no then you can't allow them to set it up at all.
Regards
Nigel