Can a family arbitration agreement specify which country's or religion's law applies to the dispute?

Not in a way that produces an enforceable family arbitration award under Ontario's framework. For arbitration to count as binding family arbitration, capable of producing an enforceable award, the decision generally has to be made applying the law of Ontario or another Canadian jurisdiction, not the law of a foreign country or a religious legal tradition on its own. Parties can't simply designate a different governing law for the substance of a family arbitration the way they sometimes can in commercial arbitration between businesses.

This doesn't stop couples from voluntarily agreeing to resolve their dispute according to religious or foreign principles as a private, personal matter; it just means that outcome won't carry the legal force of a family arbitration award, and won't automatically be enforceable through Ontario's family court system the way a properly conducted Canadian-law arbitration would be. If a couple wants both religious or cultural considerations and genuine legal enforceability, a family lawyer can help structure an approach, such as a properly formed domestic contract informed by those values, that achieves both goals rather than choosing one over the other by accident.