The short answer is yes, you can use topical minoxidil while taking Accutane. There are no contraindications for that. The longer answer is below.
There are two issues going on here:
androgenetic hair loss, with a hereditary component from your father's side of the family
hair loss due to Accutane, a type of temporary hair loss, called telogen effluvium
Androgenetic hair loss, also known as male pattern hair loss, is primarily hereditary. Hair growth happens in cycles.
Anagen - the longest portion of the cycle, the active growth phase. It ranges from 3-10 years and approximately 90% of hairs on the scalp are in anagen.
Catagen - a short transition phase, about 3 weeks, at the end of anagen.
Telogen - a resting phase, lasting approximately 3 months, at the end of which the hair in that particular follicle is shed and is replaced by a new, growing hair (anagen, again). Approximately 10% of hairs on the scalp are in telogen at any given time.
In androgenetic alopecia, the hair cycles procede normally, but under the influence of hormones, primarily dihydrotestosterone, the hair is miniaturized with every cycle, becoming finer, thinner and shorter, until ultimately it doesn't show above the surface of the scalp. So hair is not actually lost.
Medications such as topical minoxidil help maintain the hair growth, although it is not quite clear how. We know that minoxidil opens up blood vessels, but that is not the whole story. Minoxidil's effect on hair was discovered accidentally when it was noted that when minoxidil was given to patients with high blood pressure (it is a blood pressure medication), they started growing hair. Everywhere, not just on the scalp. So minoxidil in its oral form is not used for hair regrowth. It's applied topically to the scalp twice a day.
Minoxidil helps regrow hair in approximately 30% of patients and maintain the hair they have in 60-70% patients. Patients with recent onset androgenetic hair loss respond better than with long-standing one, and women respond better than men.
In telogen effluvium, there is a stimulus, be it medication (as is the case with Accutane), illness, severe stress, surgery or a number of different reasons, for a large number of hairs on the scalp to be converted from anagen to telogen phase. That is followed by increased shedding as the telogen hairs do fall out at the end of their resting time. The onset of shedding is approximately 3-6 months after the onset of the stimulus. These hairs generally grow back.
In patients with androgenetic alopecia that are experiencing telogen effluvium for whatever reason, the hairs that are being shed are being replaced with finer, thinner hairs. So there is some permanence to the telogen effluvium in this case.