First, you could set expectations that all questions are invited but you will record the conversation (or video call) and reply with an organized response to code questions. You are free to ask whatever questions you want to. This limits questions you must answer on the spot to things like availability, etc. You probably know those answers comfortably. If they balk, just ask them to trust you. Then make sure to deliver. A helpful skill is to always be comfortable to say "I will get back to you about that." If you don't feel free to say that, the anxiety might be from not knowing what it is like when that is said. In that case, try it. It's a normal thing in my opinion.
And from what you are saying, they will notice the difference if they don't take you up on your request. Be proactive so it's their choice if they decline your request.
Second idea, for remote work, is to respond via recorded video. I have clients send me recorded video of their questions and activity on the screen. It works well because it's personal and it's async. When first starting out, people hiring do need to see a face and hear a voice. This is a useful next-best option.
Your situation sounds challenging. Your desire to discuss it is commendable.