I'm sorry Ty is soiling right outside his litterbox and sometimes, his stool has blood in it.
Since you have a new kitten in the house, Ty may feel stressed from the change and in addition, is 'marking' outside the litterbox, which is instinctive when a new cat enters the household.
The occasional blood in his stool could be caused by stress, or he might be getting in the kitten's food when you're not around. Typically, blood (and sometimes mucus) in the stool happens from time to time and it's usually nothing to worry about. Fresh, red blood in the stool is called 'hematochezia' and can happen if Ty is straining to defecate, or he's irritating blood vessels in the anus or rectum.
If he is stressed, you can get some Feliway plug in diffusers; these emit cat calming pheromones and have no scent to humans.
Blood in the stool can also be caused by a food allergy or the ingestion of some non-food material like the piece of a toy, so check that all his toys are in one piece. In a young cat, blood in the stool can be caused by intestinal parasites, so it would be advisable to have a fresh fecal sample analyzed by your vet. Here is more information:
Try changing the litterbox and/or the litter you're using (use an uncovered box and unscented litter) and even change the location of the box and see if this makes a difference. The box should be in a quiet, low-trafficked area of your home. If the kitten and Ty are using the same box, you'll need to add another box, as most cats don't like to share.
It's important that you clean the areas where he has soiled, with an enzyme-based cleaner, like Nature's Miracle, Zero Odor, Odor Mute and many others you can find in your pet supply stores.
It would be advisable to have Ty evaluated in person by his vet and in addition to the fecal sample (try to bring it with you, to save time), a urinalysis and routine blood work may be suggested.
I hope all will be well with Ty and please let me know how he's doing and what the vet's findings are. Thanks!
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