I’m not a doctor. I’m not trained to diagnose mental health conditions or prescribe medication. I’m a psychotherapist, a non-medical mental health professional. I have various professional qualifications, including an MSc in psychodynamic psychotherapy.
My opinion above is based on personal experience of working with people aged 14-25 some of whom were affected by the situation you describe. It’s also based on the knowledge that consistency is absolutely key in making children feel secure. Even a consistently mildly neglectful or unkind environment is more reliable than one where the care givers are erratic or switch from kindness to indifference - consistency means a child knows what to expect and can adjust their expectations of life and relationships accordingly. Inconsistency means they can never know what will happen next. That’s why the sort of situation you describe can be so disturbing for children.
Since I don’t work with them into adulthood I can’t tell you what might change for them if their parents stayed together long term after reuniting. They might eventually lose the unconscious fear that one parent might leave and shatter their world again but I think it would take many years and probably some family therapy for them to fully trust the situation.
I have also trained and worked in couples therapy (although I don’t do that now). IME couples who split and reunite will often split up again and often quite quickly, within a couple of years. The issues that caused the original breakdown of the relationship don’t disappear and after the euphoria of the reunion passes they can rear their heads again.
I’m not saying a successful, long lasting reunion is impossible. If one or both of the partners have managed to make important changes to themselves such as giving up drink or attending successful anger management classes or undergoing some sort of counselling/therapy that makes them a more understanding partner or helps them deal with past trauma then it can be done, but it isn’t easy.
I don’t know if any of this is any way relevant to the situation that has made you pose your original query but if it is something you are considering for yourself, be aware how difficult it might be for you and your DC. Getting some sort of counselling, either as a family unit or individually might help make the transition easier for everyone involved.