Good question. I am not aware of any grammar rule that would answer your question. However, some people would say that the infinitive form of the verb "let", i.e., "to let" should not be broken up, therefore, if we follow this idea, the better choice would be "... just to let...". If the infinitive is broken up into "to" and "let", with another word in between the two parts of the infinitive, it would be called a "split infinitive", and some people object to splitting an infinitive. Here's an better explanation: http://www.oxforddictionaries.com/words/split-infinitives

I agree with Ben that the expression should be "leave her alone". Perhaps you confused it with "let her be"? That sounds slightly formal. You might say "Just leave me alone!!!" if you're angry and irritated. If you put that in a full sentence, I think it still carries that "annoyance". I'd say the first sentence reads more smoothly, with the "tone" you intended to give. "I thought it was a good idea just to leave her alone."

1. The correct expression is "leave her alone". 2. The principle of "not splitting an infinitive" should by and large be observed. So the preferred, or more elegant, option is "...just to leave her alone".

I felt that either was all right. I thought of the second sentence whenever I tried to put "just" this way. I always ended up skipping "just".

mmm I really don't have avertified answer based on rules but I feel it the second sentence is more easy to say and familiar