Honestly, I think that children with mental disabilities should not be required to learn a second language until well after their L1 has been firmly established.
Controlling code-switching behaviour can become a nightmare later on, and it really just ends up confusing and hindering their communication skills.
Personally, I would do my best to provide a safe space for the child, reduce stress triggers to the best of your abilities, and focus on teaching English to the kids who it would actually benefit from it.
Special needs students here in Korea often fall through the cracks, and its heart-breaking to see students denied the help they clearly need because their relatives don't want to admit that the extra help is needed, but as a NET, we neither have the training, time, or support needed to actually do something. In some memorable cases, we can actually be punished for making the effort. On the bright side, special education in Korea has been making huge strides forward over the last decade or so. I have seen special needs kids go from being shunted to the back of the class and told to just be quiet to the implementation of tailored programmes and the introduction of qualified care givers to assist them in the classroom. I think that despite the social stigma that mental disabilities still carry, Korea is well on the way to catching up with the West in taking care of its more vulnerable demographics.