Thank you for writing. As difficult as it may seem, what you should do is mind your own business. You are living at your parents’ home to save money, not to be an in-house therapist. Your parents are going through a rough spot. You can share your concern in a loving way once, but then it’s up to them to figure it out. You are not in the middle of their relationship unless you put yourself there. In fact, if you try to be a counselor, you may unintentionally reduce their motivation to work with each other.
My guess is that they both know why they are distant with each other. Maybe they think that if they don’t talk about it, it will blow over. Maybe they’ve been through this kind of situation before. Your mom seems to have a strategy for managing (not letting it affect her). Your dad may be also engaging in a strategy he’s used before. They haven’t yet decided if they want to get into some couples therapy to deal with whatever it is. They may not think it’s necessary or they may not be ready.
My best advice to you is to go about your own business and leave their relationship to them. You are sharing their home but you don’t really live there. You’ve been an adult on your own too long for that. Maintain a normal loving relationship with each of them but don’t talk about what is going on between them. Go to work. Go out with friends. Help out with household chores, of course, but work on maintaining an independent life even while you are dependent on your folks for a place to live for awhile.
I wish you well.