Tomcat and Brendricky have both given some good information.
You must first rule out medical causes of the inappropriate urination. Have blood-work and urinalysis performed. Excessive and/or inappropriate urination can be caused by diabetes, thyroid and other endocrine disorders, kidney disease and of course urinary tract disease or infections. Once these have been ruled out than all that is left are behavioral diseases.
You should have at least one litter box per cat, plus one additional litter box. They should be kept spotless at all times.
Many cats are fearful of changes in the environment. It sounds like the environment at your home is constantly changing and difficult for your fearful cat to tolerate. There are some things that you can try at home. Purchase Feliway Infusers for all the rooms your cat has urinated in. Feliway is a feline pheromone that gives cat's a feeling of well being. It may be enough. You can also brush or sponge it on the areas that your cat has soiled.
If Feliway is ineffective there are over the counter tranquilizer's that may help. Another possibility is Bach's Rescue Remedy. One or two drops given orally one half hour prior to the new infants entering your house may help.
Shen Calmer, a Chinese Veterinary herbal formula may also help. It is available from Dr. Xie's Jing Tang Herbal Company by prescription from your veterinarian. There are also non-herbal medications such as Prozac and Paxil and others that work very effectively for cat's if the herbals and Feliway are ineffective.
Lastly, behavioral modification under the help of your veterinarian would also help.
Sounds to me that there is possibly a cat in the home of the babies or at least one of them. Your cat sounds like it is marking his territory. If your cat smells other cats on the infants it can feel threatened. The cat could also be jealous of the babies. The babies are now getting all the attention and your cat no longer is getting as much attention as before. such as maybe being shooed away as to not accidentally scratch the baby. Your cat has feelings remember that. Just my thoughts on the matter.
I am sure an expert will answer you shortly. But thought I would give you some suggestions that might help until one can respond to you.
Hope all turns out well.
Bren
Hi...sounds like you have a handful in your house! To be certain, many cats are very tempermental about their environment and changes can cause inappropriate elimination. I am sure one of the experts will answer you shortly, but I wanted to maybe help by asking a few other questions:
How many cats total in the house and how many litterboxes?
Are all the cats neutered/spayed?
Do any of the cats go outside?
Does this particular cat ever urinate inside the litterbox?
Is this cat urinating on a horizontal surface (the floor) or backing up to a vertical surface(like a wall)?
The first step you should consider is taking this guy to your veterinarian for an exam and a possible urinalysis. He could have a medical condition that is causing the inappropriate urination. If he doesn't have a urinary tract infection or other medical condition, you can start looking at behavior issues.
Good luck!
Tomcat