Correcting interactions with another parent

Should I be correcting my children when they don’t use skills with their dad? My husband often starts power struggles with our children. He agrees with my using TSG but does not do it himself and is not motivated enough to learn the skills. So very often he uses harsh tones, manipulation, and says he wants them just to do right because it is right. So my children don’t use the skills with their dad. Very often they will end up arguing or talking back to him. Should I correct them? In the past, my interference has only led to more confusion. They get mad and say that their dad wasn’t using the skills or their dad started the bad interaction and so they don’t have to use skills with him. I’m just uncertain what to do. I wish my husband was more motivated to want to really dig in and learn and apply this but I’m running out of hope that he will. I’ve been at this now for around 3 years.