So how do I diplomatically deal with Jane D's this habit of continuously delivering political speeches in private?
Don't argue with Jane. Don't offer counter-arguments, don't say that you are on her side. She's already proven that she won't listen to any of those and isn't open for a 'nice' debate.
'Nice debates' follow rules. One of those rules is the ad hominem fallacy. This is what Jane is doing: 'You men' is an ad hominem fallacy. Cut Jane off. Simply state that you are not willing to discuss politics when she keeps making obvious mistakes like ad hominem fallacies. Cut her off every time she does this. Don't let her gain momentum, cut her off immediately, as soon as she says the 'you men'.
Mother has also requested me that I should not tell Jane D directly not to discuss politics when she visits us, because it is impolite from the point of view of 'Indian hospitality.'
The above solution should work. It cuts Jane off, so the discussion should be done. And you're not telling her to never discuss politics, only that you're never discussing politics with her when she's not honoring the rules of debating.
###Note after seeing all of the comments:
Note after seeing all of the comments:
There are a lot of comments saying that Jane doesn't want a debate/nice debate or will get pissed off.
First of all, the way I read the question Jane is already ranting and pissed off with OP being a male, and thus I myself am not too worried about my solution 'pissing her off'. She's already past the point of being nice herself in my opinion. It is something OP should take into account, however, and only OP can do that since they are the one that is meeting with Jane and getting an impression of her mood.
Second, the point here was that OP can't say "I'm not discussing this/politics with you" directly because that would go against mom's orders. So my solution is to state that he's not discussing this because Jane isn't following the rules of a nice debate AND to follow through on that, so no talking (basically walking out on the discussion), until Jane brings these things up in a nice manner. The way I read this question, the OP isn't adverse to discussing these topics with Jane, but it's the way that she's discussing things that bothers OP.
And last, yes, Jane may or may not be making ad hominem fallacies. I read the question as stating that every counterargument the OP made to Jane was dismissed on the ground that he was male. And that is an ad hominem fallacy.