In the world of "Julius Caesar", women are kept within the domestic sphere. Why?
First thing to say is - I think - that in "Julius Caesar" women are very usually confined the domestic sphere. Yet, the play is one of Shakespeare's most political, and it really doesn't focus very much at all on the domestic world of its characters.
There's a domestic phrase in the play - made up of two consecutive scenes, Act 2 Scene 1, and Act 2 Scene 2. Both scenes show women desperately trying to break through to their husbands who, though their physical location is their domestic homes, are actually engaged in conducting political business.
Brutus, in Act 2, Scene 1, has just finished conducting a meeting of his conspiracy in his orchard, when Portia interrupts, desperate to know what is going on. She knows that something has been bothering him recently, and she wants to know the secret:
Within the bond of marriage, tell me, Brutus,
Is it excepted I should know no secrets
That appertain to you?
She even goes as far as marking herself on the leg to show her own bravery. Brutus, interestingly, does tell her - though it seems to send her slightly mad.
Caesar's wife Calpurnia literally stops him from going to the senate, because of the dreams she has had:
O Caesar! These things are beyond all use,
And I do fear them.
She actually halts political business - until Decius Brutus comes in, reinterprets her dream, and Caesar changes his mind. Calpurnia never speaks again - or appears again - in the play.
So both women attempt to tread into the political sphere. But neither of them really benefit from it at all - Portia manages to get a tiny bit of political knowledge, but it doesn't help her - and though Calpurnia's influence, for a moment, looks like working, again, it really doesn't last.
So women - in this play - aren't totally kept in the domestic sphere. But effectively, they might as well be.