Can I file for Medicaid with showing 1 person as me in the household as I will not be included in their tax returns?

If you are a non-citizen or green card holder that has been here under 5 years, it gets even trickier. Certain refugee groups or individuals from certain countries may get waivers of eligibility.
Resources Information on non-citizen eligibility, application, and verification for Marketplace, Medicaid and CHIP eligibility
https://www.healthcare.gov/immigrants/
Information on Medicaid and CHIP eligibility for non-citizens
http://www.medicaid.gov/medicaid-chip-program-information/by-topics/outreach-and-enrollment/lawfully-residing.html

You can file for Medicaid as 1 person if they are not including you on their tax return HOWEVER the money you have been paying them to live there should have either a written care agreement/share of expenses in place that tracks the money you give them or a rental agreement that matches them declaring the rent of $500 per month. Medicaid requires reporting of income and expenses, living, medical and otherwise, and can have a 5 year look-back of financial records (bank, pensions, social security, any sale of assets like house and where money went, etc). Many states also include MERP Medicaid recovery for any one over 55 that receives Medicaid benefits. My state is one of them.

From what I understand Medicaid is based on your assets alone, not your D/SIL's assets, whether or not they include you on their tax returns.