I live in Washington state. I am mandated to cover my dependent child on my health insurance by divorce decree. I qualify for health insurance through my employer but it is over $400/month and the deductible is $6000/person. I make $30,100/year and I can barely afford food due to the insurance premiums. I am allowed to claim my dependent on my tax returns every other year starting with 2015.
Would it be less expensive for me to get insurance through the exchanges and how can I do that if I don’t claim him on my income tax every other year?
If a dependent has access to affordable employer sponsored coverage they can't get ObamaCare's cost assistance, but can qualify for Medicaid / CHIP. In your case, due to income, you don't qualify for Medicaid / CHIP and because you have employer coverage don't qualify for Marketplace cost assistance. Since you have a dependent under 19 your employer must offer coverage. Therefore the only way you could get around this all and use Marketplace cost assistance is if your coverage and your dependent's coverage each exceeded 9.56% of your MAGI income.
Since you are responsible for covering the child it wouldn't make sense not to claim them. You would be foregoing tax credits and tax breaks related to the child and would still have to provide coverage.