Hi Cool,
Welcome to SI. I spent most of my first year lurking too. Glad you finally decided to post.
A few things:
1. Your request that your spouse read a book with you and discuss the chapters is not unreasonable, regardless of what anyone - including your MC - says.
2. The fact that your spouse is refusing to comply with your reasonable requests because of her own shame, is a red flag in that she is still putting her comfort over yours. I'm sure you know that, and that's why you're feeling stuck so I will not belabour this anymore.
3. There is no one way to heal from an affair. The homework is going to be different for everyone. MC is less about giving you a numbered list of steps you must do to heal from the A, and more about figuring out how the two of you can communicate about your issues more productively.
4. MC can be really REALLY uncomfortable. I cannot tell you the number of times in MC where I was asked questions or challenged things that I said, that made me feel taken aback, dismissed, or misunderstood. Sometimes it felt super shitty in the moment, like it was implying I was wrong or unjustified in my feelings. Sometimes it was because she simply wasn't accepting what I was saying at face, and wanted me to dig into what my actual motivations were. Sometimes it was simply because I didn't know how to answer the question in the moment and felt silly for not being able to respond properly. I would typically feel DRAINED after MC. Sometimes, I would go home and cry, or sometimes I'd stew about the way some conversation went, or I'd be mad that my husband didn't stick up for me if I felt that the MC mischaracterized something I did or said. One time I was so mad, I refused to go home with my husband and insisted on walking home. It's normal to feel uncomfortable being pushed outside of your comfort zone. Usually if something makes you feel uncomfortable though, there is something to it and it's worth unpacking. I'd go home and think more about what it was that was asked, and sometimes being challenged encouraged me to look at something from another perspective and I'd change my mind or soften my stance or gain some empathy or nuance for another perspective. Other times, the the more I thought about it, the more clear I'd be on my original thought and I would be able to flesh out the 'why' a little better so that I'd be able to come back next session and explain it more thoroughly next time. You can always go back and say "I want to come back to something we talked about last time" and have further discussion.
5. Being challenged on something doesn't mean that you're necessarily wrong. Just like having strong views on something doesn't necessarily mean you're right. Often there is no objective right or wrong. An MC is not a judge who see's a disagreement between rigid viewpoints and lays down the law, declaring one person right and the other wrong. Just because the MC says something doesn't mean you have to give up on it. Typically the goal is to communicate the viewpoints to see if you can better understand one another and might be willing to try to see things from one another's perspective.
6. Consensus can't happen in an echo chamber. If you want to be told you're right, you can come here and we'll validate you all you want, but I don't know how much that will help you to convince your wife. Some people expect the MC to be a judge who will tell them they (as the BS) are right and their spouse (as the WS) is definitely wrong. They expect the MC's role to be to convince the WS of their wrongness. Some will take any challenge by their MC as a sign that the MC is a quack who is biased against them and write off MC entirely. I'm not saying there are not bad MC's out there, but I would caution you against that kind of black and white rigidity. (FYI, I'm not at all suggesting that's where you're at)..
7. You're a few weeks in. Your MC doesn't know you or your relationship that well right now. She is probably trying to get to know you, your wife, and get a feel for how the two of you each think and interact and what makes you both tick. She is also trying to get up to speed on where you are at, what the sticking points are, and why you're stuck. She's also probably trying to build rapport with both of you - your wife too. She cannot do that if she takes any one person's side all the time. In order for you both to feel invested in the process of MC, you both need to feel heard and can see things from your perspective. She knows that your wife has resisted change thus far. If your wife feels like the MC is just a third party who is going to rubber stamp every thing you say, she is not going to buy in to the process (and vice versa obviously).
8. Further to the above, I don't think the question was unreasonable - though I understand why you were taken aback and bothered by it. After a few sessions, your MC has no idea whether or not you're a reasonable person or not. She probably has some sense that your wife, wrongly or rightly, believes you are trying to punish her and she's trying to explore why she might feel that way. I know I've seen BS here who get stuck on the need to punish their spouse, so I'm sure she's seen worse. She was probably trying to determine what about the book reading mattered to you to see if there was some other way you could get what you were looking for - was it something about the books itself? Was it the act of doing it together? Was it that your wife be willing to subject herself to something she found uncomfortable in order to prove her commitment to you or to the process? If she knew what part of it mattered to you, she might be able to see if there was some way to explain it to your wife so that she might be more willing to buy in. She may have been asking simply to gage your (or your wife's) reaction to the question. Your wife may have heard what she wanted to hear, but that doesn't mean it's true and it doesn't mean that you wont come back to it.
9. I hope you don't take this the wrong way, but it's worth considering whether there is some kernel of truth to the question. I know that in the early days of R, there were certainly times that I wanted my WH to do things that pushed him out of his comfort zone in R because I wanted him to feel uncomfortable. Like I wasn't being abusive or punitive, and it wasn't the ONLY reason I wanted him to do the work, but I wont deny that my desire for a bit of penance played a role. If you had asked me then, I'd probably have balked too, but for me, it's true and I don't think there is anything wrong with admitting that.
10. It sounds like what matters for you is the effort. I get that. I wanted to feel like my husband was putting as much, if not more effort, as I was into healing and R. And yes, that was an impossible ask because as the BS, I spent every waking moment thinking of and obsessing about the R, in a way that my husband could not imagine. And that felt incredibly unjust and lonely and I wanted someone to share the burden of that with. Over time, I realized that what mattered more than any specific homework item, was that he was doing something. With that in mind, I remember that when we ended up stopping MC and my husband took a step back from IC, I resisted for a bit because it had been a measurable way he was demonstrating effort (and penance!) to me. Part of me was afraid if he stopped going, he'd revert back or would stop growing, but also I was worried that if I agreed we no longer needed to be going to MC, it was almost like I was agreeing that the problem was over and solved and I didn't feel that was true.
Anyhow, this was a bit of a novel and I apologize for that, but you never know who may be lurking and who may benefit
I appreciate some of it may not be applicable, but as always, take what you need and leave the rest.
Best of luck.