I was wondering if Muslim women are allowed to work outside of their home? Are there conditions where it is allowed? What if the husband's income isn't enough for the family?
I am no scholar, but the wives of the Prophet PBUP "worked". Hazrat Khadeejah was a successful merchant. How she conducted her trade, I am not sure, but it would be fairly difficult to be successful without enforcing some sort of authority, which meant it would require her presence or interaction with her hirelings.
Hazrat Aisha was a scholar. Scholars, do not live in a hole. They interact, albeit this kind of interaction can always be done behind a screen of sorts.
So the precedent is there, the only question is how to go on about it. For that Scholars have put forward their opinions with arguments. If this matter is dear to your heart, don't only look at their final statements, look at their arguments as well and decide accordingly.
A Muslim woman must not be excessive in going out from home unless it is a valid necessity that cannot be fulfilled unless she goes out. So, if she has need to go out, she must observe proper hijab. However, if a woman is able to stay at home, that is better and protective for her. Allah addressed His Prophet's wives-who are our role models -
"And remain in your homes." [Al-Azhaab:33]"
This is also reiterated when we read that Allah loves it when woman prays at home and doesn't go to masaajid though masaajid is the pure place for prayer.
The Prophet (salallahu alayhi wassalam) said: Do no prevent the servant woman of Allah from going out to the masaajid of Allah. But their homes are better for them." [Muslim no.442]
However, Scholars of Islam don’t restrict a woman from working outside of her home. In fact, there are jobs where women are required. For example, teaching women or female gynecologists, nurses etc. There is nothing wrong in that as long as she abides by the following guidelines :
She must have a need for doing this work or the community she lives in requires her to do this job, such that there cannot be found any man that can do the job.
She should do this after fulfilling the job she has at home, which is her primary job.
This job must be in an environment of women only, such as her teaching women (only) or doctoring and nursing female patients. And her work must be separate from men.
Likewise, there is nothing that restricts her from learning the affairs of her Religion – in fact she is obligated to do this. And there is nothing preventing her from teaching about the aspects of her Religion, so long as there is a need for that and her teaching is held in an environment of (only) women. And there is no harm in her attending classes in a masjid and so on, while being consistent in that and segregated from men. This can be seen from the women in the beginning of Islaam (i.e. the Sahaabiyaat), in that they would work and study and attend the masaajid.
Also, since nowadays there are opportunities to work for a concern from home, this is good. It is also allowed by Islam provided she fulfills the job at home.
 From Tanbeehaat ‘alaa Ahkaam takhtassu bil-Mu’minaat (pg. 6-11) by Shaykh Salih Al-Fawzaan
As long as she doesn't violate the code of conduct and rules of Islam made obligatory upon her, such as:
- how should one interact converse with a non-mahram *
- the dress code she should follow *
- rights of husband are not negatively affected
- husband's permission
- parents' permission (could be mistaken here)
- surety that one's faith will not be at risk *
- business doesn't involve haram dealings or things that are prohibited. E.g. wine production
then it is perfectly halal.
* same applies for men.