Aside from the awesome posts before this one, think about what is the obstacle in the novel that could have made Esperanza quit. The obstacle was communication, namely, how her lack of English skills made her and her family quite powerless. However, once she learns the language, she gains back her power because she is in control of the strongest weapon that can make or break human relationships: communication. 

So, for your essay, just name the obstacle for what it really is so that it is no longer considered "too general."

It would begin with

Lacking the power of communication

Then, add what is the result of lacking the power of communication. It should read:

Lacking the power of communication disempowers and disenfranchises immigrants, such as Esperanza.

Then, complete the thought by stating either a solution or a closure to this situation. It could read: 

Lacking the power of communication disempowers/disenfranchises immigrants such as Esperanza. Gaining control of the language will bring empowerment back to them. 

Language learning, identity, cultural differences, social inequalities and feelings of inadequacy are the prevailing themes that permeate throughout the novel. If you focus on one of those issues, and simply define them for what they are, you should achieve a strong thesis statement that does not repeat verbatim the words of the teacher and, at the same time, shows that you can understand the novel at a deeper level.

A theme statement explains a key idea or subject presented in a book according to what the author is saying about that subject.  A strong theme statement can be applied universally (as in, it does not relate only to the plot of the book) but is not so general that it could be said virtually anywhere.  Finally, it must be proven with examples from throughout the story.

Reading your theme statements above, the "too weak and general" comes from the fact that these are statements which could be applied to almost ANY novel, not specifically House on Mango Street.  Working with what you have, I'll give you some pointers.  The key is to be as specific as possible without adding plot details to the theme statement.  I encourage my students to think in terms of cause and effect, which you have attempted to do.  Writing strong theme statements is definitely a challenge, and practicing will only make you better.

"Hardships and negative experiences in life can make a person become stronger."

Cause: What kind of hardships?  What kind of negative experiences?  Make a more specific category of hardships and negative experiences.  Effect: "Make a person stronger" is a cliche.  Exactly what happened as a result of characters' hardships?  Choose stronger verbs.  Consider exactly how the hardships made people stronger.

"Obstacles can make a person fall into despair and stop trying."

Cause: what kind of obstacles?  Again, provide a more specific category that can be proven with various textual examples.  Also, you might be able to specify what kind of person here.  Not all people fall into despair as a result of hardship.  (The book actually proves otherwise.)  Effect: again, think about exactly how the obstacles destroyed characters.

From the sound of both these theme statements, you might have a compound idea going on here.  Perhaps you could use something like

Although __________ obstacles cause __________ people to fall into despair and give up, the same __________ hardships and negative experiences make ________ people stronger.  (*Note: do not fill in the blanks with characters names or plot details.  Use descriptive adjectives.)

Now you have set yourself up to write about the different types of characters: those who gave up and those who did not.  This sets up an essay which will compare/contrast characters in addition to proving a theme.