I had 4 cats when I brought my son home from the hospital, 15 years ago. never had a problem with him getting into the litter box. Litter boxes were not kept in the common rooms of the house (I did not have a garage), but on the porch that the cats accessed through a bedroom window, or in an odd corner out of the way of toddler ramblings. Baby gates were effective deterrents also. Oh, dogs and litter boxes - yeah, yuck - but the same rules apply for keeping dogs out of litter boxes that apply to keeping toddlers out of litter boxes. LOL
Over the years I have lost pets, and added pets, introducing new animals to the house. Whenever I do so, I give the new animal a separate place to be - usually the family room in our house now - complete with food, water, litter box, and limit the other animals access to the room. The existing animals wander in, check out the new one, the hiss, growl, leave - this repeats for days. The new one ventures out when we take the other animals off to bed and slowly explores. Eh, in about two weeks everyone has found their own level and it works out.
Neutered male cats, IMHO, become lovely pets. Cats, to me, are easier pets to have than dogs (and we have 3 cats and 4 dogs), because they are more self reliant - a litter box, food water, and they are good to go. Do scoop the litter box at least twice a day - I like the clumping litters or the Breeze system, over the regular kitty litter. The garage is a great place to "assign" to the cat - it will give him a place to get away and keep the litter box out of sight. As for the dog, they will either get along, or not - unless they actually fight, just let them be. I have one cat who loves the dogs and whom the dogs love - the other two cats just ignore the dogs.
Your child will learn to interact the with the cat - teach your child how to pet the cat, let your child put the food down for the cat (good way to teach the difference between people food and cat food). Since you already have a pet - your child is already acclimated to pets so the transition should not be that difficult.
Oh, and you don't train cats. LOL They acclimate though. It may be that after years of being outside the cat will love being a daily part of the family. If you are worried about him getting out, get him a collar and a tag, and have him chipped. I had one, years ago, that was a stray that we took in - he loved to go out and since he was familiar with the neighborhood I let him - he always came home. When we moved into an apartment he became an indoor cat. He adjusted really well to not going out anymore - being in a new place helped I think. He spent his remaining years with us, into our new home, as a fat, happy, indoor cat. Your kitty may well not have an issues with being kept indoors.
Good Luck
God Bless