How would you treat recurrent endometrial carcinoma with a presentation of inguinal and external iliac adenopathy?  

I would treat with definitive intent with either surgery followed by (chemo) RT or definitive (chemo) RT targeting the pelvic at least up to the common iliac and bilateral inguinal region.

Presumable post-surgical recurrence without receipt of previous RT. Is there a vaginal recurrence as well in or extending to the distal vagina, which could explain the inguinal nodes? Are the nodes PET-positive or biopsy-proven? If this is purely a nodal recurrence, no reason to think distal vagina...

If not already done, I would get PET/MRI and do an EUA with gyn onc to rule out vaginal recurrence as @Ashwin Shinde noted.  Then I would treat with definitive intent RT with chemo if able. I would follow that with carbo taxol if tolerable +- IO with consideration of MMR status.