Must I be frank with my brother and apologize to him so that Allah accepts my repentance after shunning him for a year and a half?

If your brother continues to commit lying and deception, you should gently invite him to repent and adhere to truthfulness and trustworthiness, because lying and betrayal are major sins. If he repents, you should affirm him in the truth. As for apologizing to him, there is no fault in it as long as the benefit necessitates it for him to accept advice and strengthen affection. Shunning him is not a sin if he deserves to be shunned due to lying and deception. The principle regarding shunning people of disobedience is to consider what serves the greater good; shunning might be beneficial in deterring him, or leaving him alone might be better if it increases his persistence in wrongdoing. Allah forgives the sins of the repentant, no matter how great they are.