Recently, I participated in a FIDE-rated tournament where the (only) arbiter had their son playing in it. I find that very odd. Is it allowed? What if the arbiter favors their kid? What should be done?
The FIDE arbiters' Commission disapproves very strongly of arbiters playing in the same competition that they are arbiting in but does not ban it.
My own federation told me when I was still qualifying as an arbiter that I may not play in any tournament at the same time that I am arbiting a FIDE rated event. So, for instance if there was a FIDE rated tournament taking place alongside a national rated tournament then I may not play in the national rated tournament and arbit in the FIDE rated one. I am allowed to do the reverse.
The ECF, the federation running chess where I live now, does allow playing and arbiting in the same tournament whether FIDE rated or not.
From what I have written it should be clear that there is no problem whatsoever with every member of the chief arbiter's extended family playing in the same tournament that he or she is arbiting. Arbiters are required to be impartial and this applies whether it is with regard to family members, friends, lovers, bosses, work colleagues, etc., etc.
What should be done?
The best advice I can give is to try not to be too paranoid. It will affect your chess playing and destroy your enjoyment of the game.