The 'rent increase' issue is likely a bigger question, but the OP has not answered.
For service animals, there's authority that you can't make a tenant relocate; but I'm not aware of any such authority in any jurisdiction for emotional support animals, the presence of which could be a problem for other tenants who have animal sensitivities. The general advice on support animals in other contexts is to try to accommodate both groups of people -- those who have support animals and those who cannot be around the animals -- by offering them separate areas, but obviously that's more of a burden when you're talking about tenants already in residence in an apartment building.

