Hiya Tina,
when you say the "real home page" what page do you mean? Did you create pages outside the program also or do you mean the Shop Home page? When you initially start a new shop you have 3 pages to start with. Shop Home, View Cart and Categories. Unless you create a home page outside of the program with an HTML Editor or a Visual program such as CC's HTML Editor or Visual Site Designer, then the Shop home "is" the home page and cannot be changed.
If you created a page outside of the program that you want to setup to be the home page you need to set that up in the Your Shop settings to point to a URL (I think the last option) and give it that URL to use as the home page. Once you do that you can make the Shop Home page be whatever you want it to be, change it's name etc. ... BUT ... it will always be the "Shop" 's home page no matter what. So what you need to do is rename it to Shop Now, or Click Here to Shop or something on that order so that when people click that it will go to the shop.
When you create a page outside the program to use as the Home page (I'm assuming here that is what you did) it is only linking to that as the Home page of the site, not the shop itself. That means that when someone goes to your domain they will go to that home page not the shop's home page.
Hopefully that makes sense. Suffice it to say that the Shop Home page is still the shop's home page, just that you can put anything you want on it, just realize that it's the landing page for when someone wants to go shop. Pointing to the URL of an outside home page, does not make that integrated with the shop so the shop does not understand (for better lack of terms hehe) that it's part of another page. It will still default to that Shop Home page or whatever you rename it when you press the link to go shop.
Some people use that as the page that tells about their products, shows lots of product examples and categories etc. so that there's good content on it.
Hope that helps. I know it's not what you want to hear, but that's the way it is unfortunately.