You should be able to go from Kigali to Kabale in that day no prob. If you have issues with your flight or are running late for some reason, you can get a special hire for about 80-100K ugx (not sure what that is in Rwandan Franks, but its about $50USD).
From Kabale to Kasesse the only direct option that will put in Kassese that day is the Kalita Express bus that leaves Kabale around 3 or 4 am - yes, very early. Just be sure to go to the Kalita Express office in Kabale town that night, or call the reservations number, to let them know you want to be picked up. They'll pick you up wherever.
Also, for your night in Kabale, I recommend staying at Edirsa. They have private rooms from 6,000 UGX and it's nice. It's also a not for profit biz and the money goes to development initiatives they are involved with. They can also help you with your travel arrangements if you need more advice (no additional charge).