I strongly recommend NOT to export HTML/CSS from design applications. Rather, build the whole thing yourself.
In all of my years as web designer I have yet to see the first app that exports proper HTML and CSS. And I have to admit, I'm glad all apps I've seen do it, do it poorly in one way or another.
HTML and CSS are like clay, you morph them and play with them to fit your specific needs and those of the project.
There is nothing more gratifying than seeing the final product and say: I did it.
The fact that you are able to implement your own designs into HTML and CSS, is a MASSIVE, massive win in my book. As a designer that knows how to work with HTML and CSS, the added value someone like that brings to a team is huge.
As you mention, the result of exporting from InDesign messes up the images and text. That's because a design and its implementation in HTML and CSS are two completely different processes, even though they are visually representing the same design.
Spend the time building yourself manually, it's time that will never go to waste. I can assure you that 110%.
And if you have any question or need any assistance, don't hesitate to let me know, I'd be glad to meet with you and help.