TLC, they do not have the right to raise your rent. Well the have the right to do whatever they want but you do not have to pay it. YOU just have to pay what you have been paying till you leave. YES, you DO have to pay it and don’t have the right to withhold the rent. They can still start eviction proceedings but it will not effect you, it will just cost them legal and/or filing fees. If you get a notice of eviction you can inform the landlord that you will not allow him to show the apartment because of the notice.
Do you know why he told you it would be best if you part ways? Did he hear from someone else that you bought a house? If that is a possibility then I would not play hardball with a grouch and I would be nice and show the apartment at reasonable hours as long as it is convenient to you an your spouse. If it is not a possibility and he is just plain nasty you have a choice of showing the apartment and giving the prospective tenant your name and phone number so if they have any questions they can call you. If you do this one time, he will not bring another couple up while you still live there.