In the past, I have had to deal with both issues, though not at the same time. Here is my two cents.
address the problem that is expanding first, meaning kill the termites first, especially since you believe the source of the moisture driving the mold has been addressed via the sprinklers/mulch removal. As long as the termites are alive the damage they are causing will continue to expand and a good bit of that termite damaged wood may have to be replaced. Honestly even if the mold was still expanding I probably would say kill the termites first (if you couldn't work on arresting the spread of both at the same time).
Once it is down to removing drywall, remediating mold in wall cavities, and replacing termite damaged trim/framing/sheathing/siding. After the threat of additional damage is passed I don't know that it matters much what is reparied first. If I were diy'ing or living in the house I would probably say mold first to improve air quality/health. If I was contracting it out I either wouldn't care or I would defer to my contractor(s) preference as to which order was easiest or made the most sense.
If it were my house I would not delay fumigation to open the walls first; to me stopping the spread of damage would be more important than knowing the existing amount of damage.
Finally be sure to take steps, usually by hiring a professional to treat, to prevent termite reinfestation.
Curiosity makes me ask, do you have an idea how far the termites have spread? When you say fumigation I picture the style that involves tenting a house. Which seems extreme, the last time I dealt with termites (twice in the same new construction house under a termite bond) we caught the damage early when the termites ate the trim around our windows leaving only the paint in places. Treating that level of infestation only required opening the wall beyond the damage and spraying as well as retreating the soil under and around the house. Even catching it early we had to entire sections of wall, drywall to siding, that were about 10 and 15 feet wide each and floor to ceiling and rebuild. Luckily the costs were covered under the termite bond.