Spaces are generally ignored by TeX, so it doesn't matter if you put one, two or even ten spaces after a sentence. TeX standardly puts more than an single space after punctuation. You can turn this off using the \frenchspacing command:
\documentclass{memoir}
\begin{document}
\parindent=0pt
\Huge
This is some text. This is some more text.
\frenchspacing
This is some text. This is some more text.
\end{document}

The space that TeX inserts is actually a stretchable space, and so the spacing between the punctuation mark and the following word will depend partially on the rest of the line. It doesn't depend on how you enter your source. So in the example you post, you can make the spacing the same if the text is exactly the same:
\documentclass{memoir}
\begin{document}
\large
This is my text block. I pressed spacebar twice before this sentence.
% This has one line in the source
This is my text block. I pressed spacebar once before this sentence, but the spacing is the same.
% This one has two lines in the source.
This is my text block.
I pressed spacebar once before this sentence, but the spacing is the same.
\end{document}

Notice that in this example the space after the . is different in the first sentence, since the first sentence contains "twice" and the other sentences in the examples contain "once". This small difference is enough to affect the spacing.
enteronce) in my GUI... please see my updated MWE. Thanks! – jamaicanworm Jan 30 '12 at 01:03