Is there anything wrong with renting out an aerobics gym and seeing your mother jump on the trampoline with grand kids? Seeing your married sister swing on a bar? And should I tell them that what they are doing is assur?
Can I also get the mekoros.
This is fine, and there is no prohibition involved.
There is certainly no prohibition in seeing one’s mother jump on a trampoline. There is no concern for improper thoughts etc. concerning one’s mother and therefore there is no halachic issue involved.
Concerning sisters there is also no halachic concern for improper thoughts (see Iggros Moshe Yoreh De’ah Vol. 2 no. 137), and although it remains correct to refrain from kissing and hugging (and the like), “swinging on a bar” is not something that will fall under this category and there is thus no need for stringency here.