You should have no problem with your taxes. Are you doing them yourself on line?

Both of my children get SSI and I am the only one that works and we do get to claim them both on taxes.

SSI can go very easily if you have all your documentation. You need both medical and financial documents because medically you need to prove they are autistic and disabled and financially because you have to prove family income. The more you make the less they get, however even if you make a good amount of money they still qualify for the low limit amount. Once you get SSI the child is legally disabled so it is well worth it.

Things that will help are written letters from doctors and specialists describing the child's condition but also your families struggles because of it. Them when you have the phone interview or in person interview show emotion and explain all of your hardships. Crying doesn't hurt either because you are working on their human side, trust me it works. If they think you are hiding things or you are being difficult they won't work with you, so I never recommend it.

Contact your social security office. You should also be able to get Medical Assistance to pay medical/therapies which is county.

I found this at irs.gov
Example :
you provided $3,000 toward your 10-year-old foster child's support for the year. The state government provided $4,000, which is considered support provided by the state, not by the child. See Support provided by the state (welfare, food benefits, housing, etc.) , later. Your foster child didn't provide more than half of her own support for the year.

They are still your dependents. Answer is yes. Are you working?