Is it permissible for a brother to prevent his older brother from entering the family home on the grounds that his wife does not wear the hijab, knowing that she is many years younger than him?

What your brother is doing, asking you to wait and not enter upon his wife until she puts on her hijab, is correct, and you have no right to be angry about that, for your brother's wife is not a mahram. To avoid waiting, you can call your brother before coming so he can inform his wife to put on her hijab.