Her husband has divorced her and is refusing to let her go back to his house until she has apologized to his parents
If this divorce (talaaq) that your husband gave you was a first or second talaaq, then it is a revocable talaaq. A number of rulings result from a revocable talaaq, one of which is that the divorced woman must observe her ‘iddah in her husband’s house; it is not permissible for the husband to make her leave and it is not permissible for her to leave except in the case of necessity or need, because Allah, may He be exalted, says (interpretation of the meaning):
“O Prophet (SAW)! When you divorce women, divorce them at their Iddah (prescribed periods), and count (accurately) their Iddah (periods ). And fear Allah your Lord (O Muslims), and turn them not out of their (husbands) homes, nor shall they (themselves) leave, except in case they are guilty of some some clear and serious misconduct. And those are the set limits of Allah. And whosoever transgresses the set limits of Allah, then indeed he has wronged himself. You (the one who divorces his wife) know not, it may be that Allah will afterward bring some new thing to pass (i.e. to return her back to you if that was the first or second divorce)”
But there is an important matter which we must point out here, which is that if the woman who has been revocably divorced shows any kind of mistreatment or offensive behaviour towards her husband’s family, it is permissible for her husband to make her leave his house and observe the ‘iddah elsewhere. The fuqaha’ based this on the verse in which Allah, may He be exalted, says (interpretation of the meaning): “and turn them not out of their (husbands) homes, nor shall they (themselves) leave, except in case they are guilty of some some clear and serious misconduct.” [at-Talaaq 65:1]. Many of the righteous early generations interpreted the word faahishah (translated here as serious misconduct) here as including offensive behaviour towards the husband's family. This is how it was interpreted by ‘Abdullah ibn ‘Abbaas (may Allah be pleased with him) and this was regarded as correct by Imam ash-Shaafa‘i (may Allah have mercy on him).
Our advice to your husband is to let you return to his house and to him, because he stipulated that for him to take you back, you should apologize to his parents, and you have done that.
And Allah knows best.