Israel can try to get the Palestinians to recognize Israel's right to exist as a Jewish state, but should not insist. Recognition of Israel's existence and a commitment not to fight it, as well as an end to the call for the right of return, should be enough. However, any peace treaty that doesn't recognize Israel's right to exist should not recognize the Palestinians' right to self-determination. Just like the Palestinians accept Israel because that's the only way to achieve peace, that is also the only reason Israel agrees to the creation of a Palestinian state.
Without a mutual recognition of rights, the agreement should only include mutual recognition of existence. The Palestinians can't demand that Israel will be the only party to recognize the other side's rights.