Some of the answers would be state specific as health insurance is mandated state by state rather than by the federal government. But, most likely,it is the same where you are as myself. If you are on your mom's insurance, you should not be on Medicaid. You can have your mom remove you from her private insurance plan (I'm assuming it's thru her employer) and stay on Medicaid if that's a better option and you still qualify. Your mom is likely paying a higher premium to cover you. Most employers only pay a portion,or none, of the cost to insure dependants under your mom.
I'm not sure if you still qualify for Medicaid if you live with your mom. Medicaid may want to take her income and the fact that she has insurance available, into consideration and therefore you may not qualify for Medicaid.
You will need to let the Medicaid office know of your living arrangements if they change from when you first applied (so, when you move in with your mom). If they do take her income into consideration, you could pay your mom rent (even $1 a month) and maybe then they would just consider you as renting a room from her rather than her "supporting" you. That may allow you to remain on Medicaid, which would save your mom money and I don't think you would have copays, etc.
Your mom's insurance would definately not be pleased to find out you had other coverage that they do not know about. There are laws that require insurance companies to handle claims a specific way when a person has more than one policy.
A few important things to keep in mind:
If you claim your mom isn't "supporting" you will probably need to be sure she doesn't claim you as a dependant on her taxes.
And, if your mom removes you from her plan, she will not be able to add you back on any time she wants. She would only be able to do so at the Open Enrollment period at her work. I would make sure that you will not lose your Medicaid before you drop off her plan.
It's VERY important to remember that you do NOT want to go without health insurance for more than 63 days for any reason. If you do, then when you get coverage again, they could exclude coverage for pre-existing conditions for 6 months, and in some states, pregnancy is considered a pre-existing condition.
Sorry for the lengthy answer, but health insurance is confusing! Even for myself and I work in the industry :-)