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Silastheman as others have said DO NOT restrict water from that puppy. That's one reason he got the UTI in the first place. Your skin kid did not learn to use the toilet over night and your baby bully will not learn to potty train over night. It takes time for their body to grow and their bladders to grow and in time they will be able to hold it longer and they also will learn to go out side. Set up a pin, you can by a plastic play pin for dogs at Petsmart or Petco and put his crate in there and leave the door open so he can sleep in his crate and go outside the crate to pee and poop. You can use puppy pads (but they like to play and chew them up) or use news paper for him to go on. Once he gets a little older you can do away with the play pin and shut the door at night. What we do is put a towel down and if the pee on them we just hose them off and then wash them. Once he gets about 6 months of age he should be able to sleep all night without incident. They still have accidents every once in awhile, but that's just pups. Be patient and he will learn as he gets older. We have a 7 month old at home and she does pretty well most of the time but will still sometimes pee on her towel. They are pups and it happens. Just remember, they are babies, just like your 19 month old, it takes time for them to learn, so please be patient with him. All they want to do is please us and be loved and will give you years of unconditional love in return.
Plus, doggie doors are not a good idea for bullies, unless you are home all the time and can watch him all the time. They will go out to play and sun and can get too hot and may not come back inside and before you know it, you have a dead bully from heat stroke. It happens all the time, so be careful if you have one.