Chorkies are a hybrid dog and are a chihuahua/ yorshire terrier mix. They ae actually bred to cancel out problems that chis and terriers have. THey have been bred since the early 90's.
In any case they are a high energy, known for being healthy, very intelligent and affectionate dogs.
YOu can "litter" train them but not with kitty litter. There is special litter for dogs. You can also pad train them. But YOU will have to train this dog.
As you have a two year old you are very busy. And your child is still very young. Too young to fully understand how fragile these dogs are. These dogs are also posessive and can become snappy with small children if they see them as 'less than' in the family ''pack''.
I have six children. However when my 1st was almost 2 my husband decided to bring home a very tiny chihuahua. He was sweet but LOTS of work and I found myself resenting him because I was pregnant and dealing with a small child and the dog just became too much. The dog was not getting the full attention he needed...so we ended up giving him to an older couple who could love and spoil him like we couldn't do at the time.
My oldest is now 18 and my youngest 9 and we have a 7 month old chorkie. WHAT A DIFFRENCE. Thinking these things through and waiting for the right time in life is essential.
My husband is like yours when it comes to accidents in the house. So I read all I could on positive training and realize that its the owners fault if the dog pees or poops ion the house. Knowledge and consistance is key. Just like with children.
I can tell you I am enjoying this puppy in my life 100% and nothing feels like a chore.
I think you need to wait till you have done having all your children and until your youngest is at least 8 and is old enough to understand how to handle a smal dog. everyone will benefit from you taking your time and waiting it out.
If you do decided to get a chorkie...they are wonderful. I recommend crate training right away. Read as much as you can (internet is a great resource) on small dogs. I would also get it into behaviour classes( best time is between4-6 months) but I would look for one that teaches positive training.
Good luck in whatever you choose!