Should I hand my domain over to someone accusing me of cybersquatting if they are actually reverse cybersquatting against me to get my domain?

The Anticybersquatting Consumer Protection Act, 15 U.S.C. § 1125(d), is meant to prevent the use of confusingly similar domain names with a bad faith intent to profit from that use.  If your prior use of the domain name was in connection with the bona fide offering of goods or services, you might have had a solid defense.   However, it seems that was not the case.  Among other things, it's unclear who owns domain "Y" from your description, so a detailed answer is difficult to render.  As a rule of thumb, if you are using your domain name in bad faith (which might include not using it at all), and it is confusingly similar to someone's trademark, you might have a problem.

There are 2 ways an accuser can try to get your domain name transferred to them: through the Uniform Dispute Resolution Procedure (UDRP) and the Anticybersquatting Consumer Protection Act (ACPA) of the Lanhan Act of the United States. The UDRP is an arbitration and you can find a searchable archive of some UDRP decisions at http://archive.icann.org/en/udrp/proceedings-archive-en.htm. You can also find searchable databases of decisions by arbitration panels at the sites of the organizations that conduct the arbitrations, for example at http://www.wipo.int/amc/en/domains/search/index.html. To win a UDRP complaint, the accuser has to show that you registered the domain in "bad faith." Published opinions tend to find "reverse domain hijacking" where the accuser fails to establish that the domain owner acted in bad faith, that the accuser regularly asserted its domain name rights, or that the primary purpose of the proceeding is to harass the domain name owner. However, each decision is decided upon its particular facts and the fact that you at one point redirected your domain to a site that allegedly has infringing material on it may be a factor in their favor. It will cost them about $1500.00 to $4000.00 to file a UDRP complaint. If they file a UDRP complaint, the World Intellectual Property Organization (WIPO) has made a model response available on its website at http://www.wipo.int/amc/en/domains/gtld/ and has FAQs available at http://www.wipo.int/amc/en/domains/guide/. Be clear that this is an arbitration and the decision will be made on what you file - you won't get to testify so your response has to be legally adequate to have a chance of winning. The accuser can also bring an action under the ACPA, which does not directly provide any remedy for reverse domain hijacking.