Is the wife obligated to pay half of the expenses incurred before she started her job, such as travel tickets and furnishing the house, knowing that the agreement was to split the expenses after she received her salary, and that her salary is indeed deposited into the husband's account?

The husband is the one in charge (Qawamah) and is responsible for the maintenance of his wife and needy children. The wife is not responsible for any of that, even if she is wealthy. However, he is not obligated to travel with his wife and children to another country, incurring the expenses of the people of that country, bearing travel costs, and increasing spending. The spouses are advised to refer to the Sharia court if reconciliation is not possible, as the husband demands things he claims are his right, while the wife denies this and claims that the agreement does not include what the husband demands in terms of travel costs and furnishing the house.