Has anyone spoken with his mother? WHY does she think that something is wrong with him? At this point, she might be feeling desperate that she is all alone in sensing something harmful going on with her son. If she doesn't have a history of being difficult or loony, then try showing some compassion for a mother who feels the need to dig her heels in. Sometimes a bio parent will just sense that something is a bit off and then feel all alone on a quest to prove that he/she is not just crazy or "over sensitive". It could be a very minor something that others would consider "no big deal"--which usually turns into someone disregarding it as "nothing"--but by the time they finish ridiculing and cutting their eyes, it's become a cause that must be won at all costs. She might not completely realize that these scans are such major expenses, if she is used to insurance covering everything. You might be surprised by how many patients request tests just to check everything out, with no idea of what is really involved.
Also, keep in mind that you are new to the party. Although you know her on some level and live with him, you cannot get inside their dynamic. You probably know ALL the reasons that their relationship didn't work and how you're so different. (I have my own ideas about that: When we don't resolve certain issues in our relationships, then we continue to attract people who will keep bringing up those issues.) I am speaking as a second wife and as a stepmother.
No two relationships are exactly alike. Maybe being married to him was a stifling and belittling experience. Maybe with him she always felt like her feelings and thoughts and perceptions weren't valid, and now she doesn't have to subject herself to that anymore. I don't know. I'm just saying to consider that you actually do not/cannot know ALL that is involved here. That awareness might help you to have a different approach with her.
I'm not sure of how you all get along, but your husband should lead this charge. As very involved steps, we don't like to be told to take a back seat, but when it comes to the law, we are not equal to the bio parents. He has two bio parents, and this is THEIR fight. If you stay on the forefront, it'll look like you are ganging up on her. Of course, you agree with your husband, so that opinion isn't really a fair one, is it?
Talk to your attorney FIRST. Get it on record that his father is not in agreement with this and doesn't want to be responsible for any part of the bill, if the scans are normal. Follow through as advised with the medical staff and insurance company. Maybe they can get an order that you all must submit to counseling before any new medical appointments--formally recommended by PCP and presented to the court.
Maybe she is certifiably crazy. Try to see her as just a mother who is fighting for her child. Even crazy mothers love their babies; they just tend to see things through different lenses. And, really, what harm is there in toning it down a bit and being gentler (still firm, though) with her?
PS. What will you do if further testing does show some abnormality? Will you apologize to her for giving her such grief? If you address it from a compassionate place in the beginning, you won't have to do any backtracking, and it makes for more positive encounters in the future, no matter what the outcome.