What are you applying for legal aid for? Is it to enforce the time limit? If so, it's not a discrimination action you need, it's possibly judicial review. Before taking JR action, you need a formal pre-action letter, and if you want to do that under legal aid it's legal aid in your own name. However, if you're self employed they likelihood is that you won't qualify, as the income levels for eligibility are extremely low. SOS SEN will do pre-action letters for parents - I think they charge, but they're much cheaper than solicitors' firms.
If you've gone beyond that stage and are looking at starting court proceedings, then that would be legal aid in your child's name and you fill in the form with all their details.
If you want to take disability discrimination proceedings for other purposes, that is an action in your name so it goes back to you having to apply for legal aid in your own right.
If necessary, contact Simpson Millar who also have a legal aid contract, and who are more clued up than Coram.