Sounds like stress. Make sure there are two more litterboxes in the house, put them in different rooms to see if maybe the new kitty will take to a different one until they become used to each other. Once Dandelion is secure, you can remove one litterbox but each should have its own +1 if possible.

If it continues for another week, take Dandelion to the vet, it may be a urinary tract infection and he associates the litterbox with pain.

Good luck, let us know how your Rag is doing. I have 4 Ragdolls, I know how they are our absolute babies and cuddle buddies so keep your eye on him.

Did you add additional litterboxes? You need at least one per cat on each level - if cat is not using the litterbox at all, you might put one behind your chair (TEMPORARILY - yeah I know, it's a PITA, but it's only TEMPORARY - idea is just to get habit re-established to go in litterbox, then move it gradually to where you want it to be.) And keep the daughter's door closed. Even if the new cat is not actively chasing your cat away from the litterbox, Dandelion could be put off by someone else using it. If you didnt do the proper gradual introductions you might want to start over and keep them separate, gradually letting them get used to each other.

Don't forget to clean out the box EVERY time he uses the box...immediately! Some cats want a CLEAN box to go to the bathroom in.
Do you like to sit on a toilet that somebody has pooped in and didn't flush?? Gross! Same idea. And as someone pointed out, it may be a UTI.
Sounds more like a 'statement', though. His owner isn't,t with him anymore, he is older and doesn't,t like 'change'. Are you giving him enough attention? You may be mad at him for pooping on your bed/chair and yell, stomp around..all actions that he is aware that are 'negative' towards him....