Try set feeding times instead of free-feeding. (This can also help with the cat's weight, as being disabled the cat will have different caloric needs and could be at greater risk of complications caused by increased weight that can come from free-feeding.)
You'll need to spend some time adjusting the cat to the idea of set feeding times if they're used to being free-fed, but the time investment will be worthwhile, and cats can and do tend to learn rather quickly. Note that if you do a switch to wet food from dry at the same time, the change may be easier.
The website FoodFurLife has some advice on switching to meal times over free feeding (though their website focus is on home-made food, the advice given is geared toward all diets, including commercial canned and kibble). To summarize the information given at their site, you will:
- Start with a large number of small meals. Your cat is used to eating on their own schedule in small amounts throughout the day; your initial meals are going to mimic this. Keep the free-feeding bowl filled during this time, but encourage your cat (gently!) to eat from the bowl you put down for meal times. Use a consistent time and a location you plan to use long-term for their meals.
- When your cat is starting to get used to the feeding times (reliably coming to eat at least a little of the food), start pulling the free-fed food. The easiest transition is to pull it during the day, and put it back at night, when the cat still isn't quite accustomed to not having food. Don't fill the bowl all the way at night, just put down a small amount, and take it up again in the morning.
- Make sure the amount of food you're providing is sufficient; if the cat is still hungry after a meal (and if their weight is currently healthy on free-feeding), increase the amount of food you're giving them. Note that some cats do tend to love food a bit more, and if they are overweight on free-feeding you may need to leave them just a little hungry. Do not drastically decrease the amount of food at any time, as it can put your cat at risk of hepatic lipidosis (aka "fatty liver disease").
- As your cat begins more reliably eating their set meals, start reducing the frequency and increasing the amount put down. Ideally you will get to 3-4 meals per day, though depending on the cat, you may end up with a little more. Three meals per day should be the minimum you aim for. At the same time, reduce the overnight food to little to nothing (or make the overnight portion the "final meal" for the day).
It's vitally important during this whole process that the one time of day you do not ever feed the cat is immediately when you wake up. Never feed your cat first thing in the morning; your cat will associate "you woke up" with "you feed me," and will start waking you for food. Set yourself a morning routine (this is good for you, too!), and find an appropriate point to feed them within that routine. For me, this is between "cleaning their litter box and refilling their water" and "getting dressed." I largely get to sleep in now in the morning because of this.
By setting your cat up with a feeding schedule, you'll be able to monitor the feeding area during that meal time, ensuring the chihuahua is unable to get to and eat the food while not creating a situation where it becomes difficult for your cat to eat. You'll additionally encourage a healthier weight for your cat (and the dog).
(Note that cats can and will learn a new schedule quickly, as well. Anecdotally, I have a cat who, for the past month, has needed a pill early in the morning. Within the first week, she associated "alarm goes off" with "I get a treat." I cannot emphasize enough how important it is to never teach them "waking up" means "food.")