Although it is true that Islam demands the Man to be the one who should support the family, But as bro, Yahya said: "It is only allowed within the boundaries set by islam"
However the baisc principle is that women should stay at home and not go out except for necessary purposes.
وقرن في بيوتكن ولا تبرجن تبرج الجاهلية الأولى وأقمن الصلاة وآتين الزكاة وأطعن الله ورسوله إنما يريد الله ليذهب عنكم الرجس أهل البيت ويطهركم تطهيرا
And abide in your houses and do not display yourselves as [was] the display of the former times of ignorance. And establish prayer and give zakah and obey Allah and His Messenger. Allah intends only to remove from you the impurity [of sin], O people of the [Prophet's] household, and to purify you with [extensive] purification.
Although this is addressed to the wives of the Prophet (PBUH), the believing women are to follow them in that because they are an example for the believing women.
Shaykh Muhammad al-Saalih al-‘Uthaymeen said that women are allowed to work in:
The field of work for women is that a woman should work in areas that women specialize in, such as teaching girls, whether it is an administrative or teaching position, or she may work in her home, sewing clothes for women and the like. As for working in fields in which men specialize, it is not permissible for her to work where she will be required to mix with men, as this is a great fitnah which must be avoided. It must be noted that it is proven that the Prophet (PBUH) said: "I am not leaving behind after me any fitnah that is more harmful to men than women; the fitnah of the Children of Israel had to do with women." A man must make his family avoid all areas and causes of fitnah in all circumstances.
Fataawa al-Mar’ah al-Muslimah (2/981).
And the Islam has provided other solutions to keep the women from working, because they have far more important role which is taking care of the husband and the kids.
On of these solutions is the hadith of the prophet mohameed PBUH:
Abu Hurairah (May Allah be pleased with him) reported:
The Prophet (PBUH) said, "One who strives to help the widows and the poor is like the one who fights in the way of Allah." The narrator said: I think that he (PBUH) added also: "I shall regard him as the one who stands up (for prayer) without rest and as the one who observes fasts continuously".
[Al-Bukhari and Muslim].
Another way, the family/relatives can support her too that way they can have double deeds:
It was narrated that: Zainab, the wife of Abdullah said:
I asked the Messenger of Allah: 'Will it be accepted as charity on my part if I spend on my husband and the orphans in my care?' The Messenger of Allah said: 'She will have two rewards, the reward for charity and the reward for upholding ties of kinship.'