Website fixing

I have a gardening blog called the blooming oasis, it got hit by a google update, and I was wondering if there is any chance anyone could help remove all the bad links and help the site to rank again.

Also I would like to change the domain name to thebloomingoasis.com/blog and wondered of this would be able to be done, as on the main domain I'm hoping to create an online shop.

The website is aimed towards the American market but I wish the site to be aimed towards the uk market instead.

If anyone can help please get in touch with me