Can I argue this point to my manager's superiors
Is going over their head a bad idea?
Can I do something else and still get the outcome I'm looking for?
The only issue that you really have is that you should not 'argue' the point.
You can go to the person above your manager, and ask them to consider the situation. It's best if you can book a time to talk to them, or if that's not really possible, send them an email.
Tell them that your manager has told you your performance is suffering because you are working remotely.
Tell them that you do not think your performance is suffering. Don't make an issue about it. Because your managers bosses job is to support your manager in the decisions that he makes.
Tell the person your reasons for wishing to continue working remotely, such as; how working remotely is helping you avoid complications because of a workplace relationship etc. Hopefully have some other reasons available too.
And at the end of whatever communication, ask the manager if he would mind being involved with the decision making in relation to this single situation, (hopefully the manager will read between the lines when you say you were/are in a relationship with your managers sibling)
Hopefully they will just agree to keep tabs on the situation, and prevent any 'unfairness' from going unnoticed.
That's about as far as you want to take anything with your managers boss, unless your manager starts behaving in a manner that in unprofessional. If there is unprofessional behavior go to HR.
Other things you should think about:
Asking your manager to help you improve your remote working performance, ask where he feels that your performance had dropped, and do things to improve this.
It can be psychosomatic, he does not 'see' you working, so he needs regular updates from you about the work you are doing.
Basically getting your managers 'impression' of why he things your performance is down, can help you 'appear' more productive to him by doing little things like emailing to update. Even though your performance had not changed, his perception of your performance will change.