Medicaid and private insurance?

You an always buy private insurance if you can afford it. That has nothing to do with Medi-Cal. You can purchase dental insurance or a dental plan. It has nothing to do with the ACA marketplace.Marketplace plans are for medical, not dental, services.

Since you are not eligible for a tax subsidy, you don't need to shop on coveredca.com.  You are able to purchase directly from the insurance companies.

TMJ is a joint disorder and treatment (excluding braces) is generally covered until medical not dental insurance.

Dental insurance is usually nothing more than a pre-paid plan.  Once you factor in the cost of coverage, Denti-Cal and private dental insurance is likely the same.

To clarify the other answers:

In California, you can purchase dental insurance through coveredca.com.  I don't know if other state's marketplace provides dental / vision insurance or not.

However, dental insurance does not come with a tax subsidy so you will be paying the same price whether you purchase on coveredca.com or direct through DD. 

There are no marketplace dental plans.  Read the plan coverage in any dental plan you are looking at.  Most require you to have had the insurance for at least a year before they pay for anything major.  Dental plans are usually quite expensive as well.  If you make so little that you qualify for Medicaid, it's unlikely you'll be able to afford dental issues.  Medicaid does have dental coverage.

Marketplace plans are eligible for government subsidies, but only if your income is too much to qualify for medicaid.  Private plans are not eligible for government subsidies, even if your income is too much to qualify for medicaid.  Because your income is low enough to qualify for medicaid, you would not be eligible for the subsidy with any type of plan.