I reside in Ca, I have full legal and soul physical custody of my 8 month old daughter. Am I able to travel freely in the state of Ca? I have to attend a 5 week job training 2 hrs. from my home. I plan to take my daughter with me where my mother will care for her. My daughter and I will be returning home on weekends for her to have her visitation with her father. Do I have to inform him of this job training if I have full soul and full legal custody? After completing the job training, my position will be in the town I currently reside in. I am not changinging any address of the child's permanent residence.

You are fine unless you have an order than specifically requires you notify your co-parent if you take the child out of the county (which is very unusual).

Review your order and just be sure you don't violate any of its conditions. It doesn't sound like you are doing anything wrong at all.