"Sorry to be the bearer of bad news, but I'm not seeing the image, even when I try to load the link directly. Looks like the link in your post here is good (yay!) but the picture isn't there? "
Gosh I don't see any link, let alone a picture. Strange ...
Re: Tiny Cat ... unlike dogs, I think cats are rather inclined to give orders rather than to take orders. It isn't easy to "teach a cat a new trick." The cat pretty much has to see it as his/her own idea.
If the night feedings are helpful, then that's a bit of hope and progress. Though it rubs her nature the wrong way, there's a decent chance that Tiny Cat will still "bug you" at 4:00 or 5:00 a.m., but only briefly and then settle down next to you, having confirmed to herself that "It's not time yet." Cats can be patient when they want to.
Re: Tiny Dog ... I reckon you're probably dealing with the same problem as parents who give birth to a second child, or a polyamorist adding a new well-entwined partner to his/her life, or anyone starting any kind of a new and highly-committed relationship when they already have highly-committed relationships that need their attention. Unless Tiny Cat be adopted out, it will become Tiny Dog's cross to bear to accept a smaller amount of time and attention from you. There's no getting around that reality. In time you'll probably chance upon better opportunities to recalibrate how your time and attention is balanced between the two pets, but perhaps right now Tiny Cat is for all practical purposes demanding the "lion's" share.
Multiple relationships (and polyamorists and monogamists both have them, for there's unnumerable platonic relationships of varying degress of intensity to consider as well as romantic relationships) will always be hard to juggle, and you have to make wise judgment calls about how many relationships you yourself can adequately juggle within your own life. Perfect balance is impossible, and perfect fairness is virtually impossible. You approach the virtually impossible as best you can, and make your own judgment call on whether you get "close enough."
The bottom line is that you're facing a difficult puzzle that only you can solve, for you are the closest to situation and the best at knowing the details of the situation and the limitations of your own mind and heart. By no means try to be "Superwoman." Just accept/pardon/forgive the limitations you have (cause everyone has limitations of a range of types and quantities), and make the wisest choices you can on how to work around those limitations. Some can be overcome in this lifetime, but others are as permanent and ubiquitous as blindness or a missing limb. So maybe you can (eventually) adequately handle two pets, in terms of giving each the time and attention that he/she wants and needs from you. Or, maybe not. That's a call that only you can make.
Non-human people, like human people, also have their limitations, and some of their limitations are lifelong too. So like Patches, if you decide to keep your cat, your cat may learn to overcome some/many of her limitations (and/or instincts if you will), but not all. At some point you'll have too decide if you can live with the stuff that's too hard-wired within her to re-wire.
I know these are hard decisions and my long-winded post probably hasn't made the decisions much if any easier.
Good luck and may love conquer all,