Incest Survivors Support Group
Incest refers to any sexual activity between closely related persons that is illegal or socially taboo. Consensual adult incest is very rare. Incest between adults and prepubescent or adolescent children is a form of child sexual abuse that has been shown to be one of the most extreme forms of childhood trauma. If you or a loved one is a survivor of incest, join the group...

if you want to project confidence to the world, a childish voice will not help you.
If it is the voice of an inner child then she needs to appear when you can give her time to express herself to you - journalling or artwork as mamoth suggests might help this (especially working with your non-dominant hand) - and to keep quiet or change her language when you are in the wider world. Talk to her about it and explain why you are insisting on correct behaviour and that you are not trying to fob her off.
If it is learned behaviour then the trick is to catch yourself doing it and stop. It won't happen over night but with time it will become easier.
Why do you think you are failing? You are overcoming barriers that most 'normal' people can't even imagine, let alone face.
I think the child like behavior is one of many things. An attempt to hold on to something that was robbed of us at a young age. For others we we hit a wall and can't let go of the child we once were. Sometimes I feel like I haven't really matured mentally as an adult. I often still feel like I'm 16.
I don't do the voice as much as I use to, I do find that certain things or people tend to bring it out of me more. When I catch myself doing it I try and make a mental note to stop. It also helps to journal about it. It's a good way to get it all out.