Thanks for your patience.
Unfortunately, if you have received a ban of 10 years for deception then your application will be rejected.
This is because deception is unfortunately taken very seriously by the home office and a 10 year ban is the largest ban that they can give.
It’s still a really long shot but if you were somehow able to prove that the original incident which gave rise to their opinion that it was a deception was incorrect then you could submit this with your application. It would most likely still be rejected but if you are certain that the application contains proof that the previous incident was misinterpreted then you could then either appeal on human rights grounds or launch an action for judicial review (both options are fairly expensive and take a long time).
These are your only options really, and neither are particularly appealing. You may consider that paying for your sister and child to visit you in the US is a more reliable way forward.
I am sorry that I could not have better news for you.
My goal is to provide you with a good service. If you feel you have received anything less, please reply back as I am happy to address follow-up issues specifically relating to your question. If you are satisfied then please leave positive feedback using the stars at the top of the page.