I agree with you. Draw blood and test. At least that will pinpoint or delete those issues.
What your vet did treated several possible things, including minengial worms. I asked about bald spots as they can appear with those....also many other issues. It's so frustrating when you can't solve the problem! We understand and as you see by replies, have most all been there at some point! It's such a matter of how possible one over another sickness could it be.
Personally, I see treatment for everything I'd suspect. You may just be in a holding pattern to allow her body to recover and adjust....won't be a week, either. I know how suffering it is for you. Hope you've separated those twins to wean! It takes far more stress on the goats body to make milk than to grow those fetus. Huge draw on their body processes. While I don't see that as her problem cause, it does interfere with her own body regenerating. There's a reason a doe gets heavily feed in a milk line.
I keep a feed on hand, Enrich by Purina. Expensive but a high powered complex of protein, vit/min. You only use a small amount...like 1/4 to 1/2 cup, topdressed to feed. Can be fed alone. High copper, too. It is not a cure but a great assist and easy to use, for animals under stress like this. Actually originated as horse supplement. Since they may be "off feed" small amount of concentrate usually is consumed, even if not a full feed amount. Also, feed her in own pan to be sure she's getting her share...goats will eat their's and another's share given the chance

Little piggish!
Please let us know how Sadie Rose comes along. We all learn and we do care!