More than three talaqs but in ignorance. Is the marriage valid? Can they remarry?

My father used to believe that if the couple gets back together within iddah, that talaq does not count and he has to give three more talaq to end the marriage. Due to this belief, he gave my mother talaq 5-6times but used to get back together within iddah period. He says he never had an intention to divorce her but always wanted to threaten her to make her follow his conditions. He recently found out that his belief was wrong and that he has given more than three talaqs and the divorce is done. He is now in doubt if he can ask Allah for forgiveness and remarry my mother? Will this marriage be valid? It is matter of life of kids, marriageable age girls and small boys. Both husband and wife really want to remarry and live together.