My landlord is not accepting my 60 day end of lease notice

You may have some options at your disposal.  The issue is whether the lease requires the 60 day notice and whether how you provided the notice (by phone and by email) constitute proper notice.  If the lease is ambiguous as to what consitutes a "written notice," I'm inclined to argue that the email you provided suffices as written notice.  However, if the lease dictates something like the written notice must be sent by Certified Mail, Return Receipt, that could be problematic.  Nevertheless, you may have an argument on that one.  Really, you need to have your lease reviewed by an attorney to get all of your options.  Something you may want to lookout for is whether your landlord seeks to charge that "April rent" by charging against the security deposit.  If it is a security deposit, it covers damages above wear and tear; however, many landlords try to use it for missed rent.  Your landlord has a certain notice procedure he or she must follow regarding the security deposit and mistakes can adversely affect your rights as a tenant.  The long short is that in its ugliest form, whoever the victor, the end point would likely be small claims court.  Generally, it is best to negotiate an amicable solution (if possible).  However, in my experience, you may find the services of an attorney very helpful in such an endeavor.