The easiest way to do this is to abandon everything we've talked about so far and simply have a form that says, "If you want to register a new domain, enter it here. If you don't, then leave this field blank."
That's what I would do.
The next easiest thing, if you really want the field to disappear, is to have a form page (call it page1.php) with the option to register a new domain or not. When they select, it brings them to page2.php (which is the information page). On that page, you include this line of code:
<?php if ($option=="Yes") { print "Enter Domain you wish to register: <input type=text name=domain>"; } ?>
That way, you only have one Information page which works for both scenarios. That make maintenance of your web site easier.
But let's assume that it's very very complicated to register a new domain and the form has to be completely different. Then you do the page2 include(a) include(b) trick that I showed you earlier. This way, page (a) can be wildly different than page (b). Then you have BOTH of those pages post to page3.php which does two things. First, it emails the contents of the form and second, it prints the Pay Pal code that you showed us.
Lastly, let's make sure you're using the right terminology. When you use the include(a) include(b) trick I showed you earlier, you are NOT redirecting the user to those two pages. You are INCLUDING the various pages. In fact, if you look at the URL bar in your browser, when the user selects their option on the first page and then gets to page2.php, they will SEE THE CONTENTS of either page(a) or page(b) but the URL bar will still say page2.php because you haven't left that page - you didn't redirect them anywhere. It's as if page2.php contained optionally page(a) or page(b) because you are including it into page2.php. This is an important concept - it's a way of making a page that can play multiple roles.
Another good example of when you might use that is if you had three levels of users: gold silver, and bronze. On every single page on your entire web site, you could include some variable content like:
information-gold.php
information-silver.php
information-bronze.php
so that you only have one web site to maintain but different people see different things depending on what kind of subscription they have to your web site.