This is a pretty bad situation.
If this is for any serious project, you need to abandon this iframe problem and just get rid of them.
Not that search engines cannot use iframes, they can, but they index what is inside the iframe, which in your case is similar to www.site1.com.
To get another site in the search engines without deleting the iframe is possible, but you will have to make a decision.
Idea
Put the URL on your iframe (othersite.com) so that it serves all the pages from site.com. Use URL redirects without redirecting URLs so that the page appears on another .com site.
Add a sitemap to othersite.com so that Google can find all of these pages.
Decision
To prevent Google from thinking that othersite.com is just a clown site1.com, you will have to block site1.com from search engines.
Block your website1.com from indexing with robots.txt
This means that any Google juice you score, such as page rank or domain aging, etc., will be lost. If this is a business that depends on search engines for business, you should think about it.
Conclusion
I have never tried this technique from my simple idea, which I had to solve your problem.
This is not a very pleasant solution, not what you need to do (if anyone else is reading this).
The best solution is to get rid of your frames. If you have problems with the inability to control html inside the header and footer frames, then there are even better solutions than using an iframe.
For example, you can use HtmlAgilityPack to parse in the html that should be in these headers and spit it out into your template with changed identifiers so that you can contain css.