It sounds like this is a problem with the way your theme is setup, since what you describe isn’t the usual behaviour of the more tag. The first part of your post suggests there’s some built-in Javascript in your theme causing the read more to expand the post text rather than take you to the single post page, removing that JS should solve it without any need of custom filters.
I’d also double check that your theme actually has a single.php template included, the latter part of your post suggests maybe not but this might also just be caused by the theme’s JS.