Does Mom keep her private insurance if she gets Medicaid?

Your mother is now what's called a "dual-eligible" -- meaning she's enrolled in both Medicare and Medicaid. That changes the other insurance she needs.

First, there's her Medicare Part D prescription drug plan. Dual eligibles need a Medicare Part D plan, but the plan your mother's had before becoming eligible for Medicaid may not be the best for her now. Medicaid will pay the Part D plan's premium and deductible and will provide her with coverage if she reaches the coverage gap (also called the "doughnut hole") for the year; she'll also have reduced copayments (as the notification letter already informed her). But to get Medicaid to fully cover her, she has to be enrolled in a Part D plan whose premium is no higher than the average premium for Part D plans in her state. If she is enrolled in a plan with a higher premium, she'll have to pay the difference between the actual premium and the state's average premium. Also, she'll have to pay the difference if her copays are higher under the high-premium plan. So, what you need to do is to find out, from the local Medicaid office, what Part D plans are fully covered by Medicaid in your mother's state, then have her switch to one of those plans if she wants full Medicaid coverage of her drugs. Because she's enrolled in Medicaid, she can switch from one Part D plan to another at any time.

As for her Medicare supplemental policy (called a "medigap" policy) from Blue Cross/Blue Shield, she probably no longer needs it now that she's on Medicaid. For dual eligibles, Medicare pays its normal share and then Medicaid covers the gaps in Medicare coverage, replacing a medigap private insurance policy. Check with the local Medicaid office about whether there is any reason for her to keep the Blue Cross/Blue Shield policy, but it's almost certain that she doesn't need it now that she's on Medicaid, and can therefore stop paying the premium for it.