Is it permissible to give a wedding dress to a woman who works in tailoring for her to rent out, knowing that I do not know to whom she will rent it or whether the renter will wear it to mixed gatherings, and will I incur sin if I stipulate that she not rent it out except to those who will wear it at unmixed weddings and she does not adhere to the condition?

The basic ruling is that it is permissible to rent out clothing, except to one who is known or strongly presumed to use it for unlawful purposes. Any garment that is strongly presumed to be used to facilitate disobedience should not be sold or sewn for someone who will use it for disobedience. If the renter's situation is unknown, then it is permissible to rent it to them. However, if it is common for the people of the country to use such dresses for unlawful purposes, then it is better not to rent them out when the renter's situation is unknown. If you stipulated to the agent that the dress should only be rented to someone who will use it for permissible purposes, then you have absolved yourself of responsibility, and there will be no sin upon you if your condition is violated without your knowledge.