All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah and that Muhammad is His slave and Messenger.
The woman is entitled to set the conditions she wishes in the marriage contract as long as these conditions serve her interests and do not contradict the purpose of the marriage contract. If the husband accepts those conditions, he is obliged to abide by them as underlined in fatwa 131714.
There is no doubt that the basic principle is that the Muslim woman should stay in her house and that this is better for her; however, this does not mean that she is legislatively forbidden from going out of her house for work as long as she abides by the relevant conditions and Islamic teachings. The money that she takes from her husband (in the case in question) is not considered a bribe; scholars defined bribes as "Money paid to evade others' rights or support one's false claims (i.e. what a person pays in order to take something he has no right to take or to evade a duty or obligation)."
Committing an act of disbelief that takes the doer out of the fold of Islam is not a simple thing that can be taken that lightly; scholars have listed the acts entailing declaring the doer an apostate. Such acts are serious, such as prostrating oneself to an idol, deliberately throwing the mus-haf in filth and the like.
When the husband is in straitened circumstances and can no longer abide by such a condition stipulated by the wife in the marriage contract, he bears no sin for that; Allaah, The Exalted, says (what means): {Let a man of wealth spend from his wealth, and he whose provision is restricted - let him spend from what Allaah has given him. Allaah does not charge a soul except (according to) what He has given it. Allaah will bring about, after hardship, ease.} [Quran 65:7] This ruling applies as far as the obligatory maintenance is concerned, let alone other than it. However, the husband remains liable to this money and is obliged to pay it to his wife whenever his financial situation gets better; Allaah, The Exalted, says (what means): {And if someone is in hardship, then (let there be) postponement until (a time of) ease. But if you give (from your right as) charity, then it is better for you, if you only knew.} [Quran 2:280]
In any case, you do not have to commit yourself to this condition. If you fear that this may constitute some sort of an obstacle to your marriage, then you can either convince her to give up this condition or consider looking for another wife.
Allaah knows best.