A given ID can be only used once in a page. It's invalid HTML to have multiple objects with the same ID, even if they are in different parts of the page.
You could change your HTML to this:
<div id="div1" >
<input type="text" class="edit1" />
<input type="text" class="edit2" />
</div>
<div id="div2" >
<input type="text" class="edit1" />
<input type="text" class="edit2" />
</div>
Then, you could get the first item in div1 with a CSS selector like this:
#div1 .edit1
On in jQuery:
$("#div1 .edit1")
Or, if you want to iterate the items in one of your divs, you can do it like this:
$("#div1 input").each(function(index) {
// do something with one of the input objects
});
If I couldn't use a framework like jQuery or YUI, I'd go get Sizzle and include that for it's selector logic (it's the same selector engine as is inside of jQuery) because DOM manipulation is massively easier with a good selector library.
If I couldn't use even Sizzle (which would be a massive drop in developer productivity), you could use plain DOM functions to traverse the children of a given element.
You would use DOM functions like childNodes or firstChild and nextSibling and you'd have to check the nodeType to make sure you only got the kind of elements you wanted. I never write code that way because it's so much less productive than using a selector library.