Without understanding the given situation, it is not possible to suggest anything. Anybody can become victim of misunderstanding. You too! Usual suggestion can be to clear the doubts with the proper analysis / reasoning or evidence before the family members. You have not commited any mistake and if you are not able to convince your family members, it is your duty to clear away the clouds and wasteful thoughts that are cropping in their minds. Relax, meditate and withdraw the power of clarity from Supreme Soul and draw the proper lines of reasoning behind the issue. Mentally radiate your positive vibrations to your family members and request the Supreme Soul to calm down the minds of your family members so that they should be able to cope with the situation and clearly understand what you want to convince. Help them to get rid of any negativity towards you. This will in turn help you in resolving the issue.
If any family member is not able to take responsibility of unwanted situation, he/she does not have such mental strength and as such, the member blames other person(s) or situation(s). Such things happen with us and it might have been occurred to any of us at some point of time when we do not have such mental strength. Low mental strength people always blame on other situation/ person(s). So, increase your mental strength and leave and ignore the issue while forgiving that person as he/she is spiritually weak and has not capacity to hold the responsibility of any situation that is unwanted and weak in spiritual values.