Proposing to his niece for his son and finding his sister proposing to his daughter for her son

Q 2: I intended to ask my son to propose to one of my sister's daughters, but I was surprised when my sister and her husband came to ask my daughter for marriage to one of their sons when they heard that someone intended to propose to her. They told me that they had wanted to ask for her hand in marriage to their son a long time before but their son's stay in Riyadh for work was the reason he could not ask for her hand before. We ended our speech with my acceptance of their proposal. I told them that we were about to ask for their daughter's hand in marriage to our son then they told me that they all expected this (Part No. 18; Page No. 434) but they were delaying their son's proposal to our daughter until we were done with our son's proposal to their daughter. When they heard that another person intended to propose to my daughter, they hastened to ask for her hand to their son before I accept the proposal of the other person. So we both accepted the two proposals at the same time. But later I remembered that Shighar marriage (exchange of daughters or sisters for marriage with no mandatory gift to a bride from her groom) is unlawful. I referred to some religious books on this issue but they did not ease my fears and doubts completely. Therefore, I decided to refer to you to explain the matter for me. It should be noted that I have decided a specific Mahr (mandatory gift to a bride from her groom) for each of them according to the regulations of the state. Half of the Mahr is paid in cash and the other half is paid in the form of gold and clothes.I hope your Eminence will end my fears and doubts; because I am torn between the desire to make these poor young people to marry and the fear of committing something prohibited by our honorable Shari`ah. May Allah protect you.