Use quotation marks for internal monologue?

Solution 1:

"This won't be easy," she said to herself.

This doesn't read as internal monologue to me at all; it reads as someone speaking aloud, but "to herself", i.e. in an undertone, maybe muttering, not apparently directed at anybody else.

If it's meant to be truly internal, I'd stick with the italics.

Solution 2:

I would say you can keep or omit the quotes for either. To me, quotes implies that you are re-telling word-for-word what was said, but leaving the quotes out implies that it doesn't really matter what the exact words were. This is why thoughts aren't usually in quotes, because many thoughts aren't formed in precise words.

If in doubt, go with the rule that if it's actually spoken, use quotes, otherwise don't.