OP, your DH might need to read up on the idea that people are different types of learners. (Visual learner, auditory learner, kinetic learner, etc.) You child may be the type for whom aural learning (I hear it, I process it, I understand it) does not work well. There is a lot of research on different learner types and how best to work with those types for efficient learning. That does not help you in the short run, of course, but it might help your husband chill a bit and realize that his child is not an ace at listening in class and then turning that listening into knowledge he retains in his head. Sometimes it's not as simple as "Just listen better in class." (And sometimes....it is.)
Meanwhile: One to two days before the test for the study guide to come home is a short time frame, I agree. I really think you and DH, without your son present, need to talk with the teacher along these lines: "When these study guides come home, no more than two days before the test, we feel we need to help Son study them. We do this by (describe how DH does it, how long it takes, etc.). We're telling you this in order to ask: Is this what you have in mind? Are we overdoing this or underdoing it? And is there a reason the study guides come home two days before a test rather than, say, a week before the test, since the curriculum covered is already known?"
In other words -- I hope you and DH can go see the teacher and lay out what you ARE doing and whether that is what SHE expects or whether you need to ramp back. Your DH and you are both frustrated but if you aren't careful you may go in there criticizing the teacher (which would only make her defensive and is not useful) and the study guides (for which she might have good reasons to do what she does; can you listen to her if she gives reasons?) and the lack of any textbooks (which is probably out of her control and a choice by the school or the school system).
As someone else noted above, this may not be as much about mastery as you and DH think it needs to be. Ask the teacher that, ask what a 2 or 3 assessment really means, ask if she is concerned or feels your son is on track. You and especially DH are now so close to this issue that you may need to hear from her that it's going to be fine and it's fine not to put in so much time.
Ask her if it's possible for the whole class to get the study guides at least a few days earlier. She likely won't do that just for your son. It's also close to the end of the year and she may not be willing to change the study guide schedule that she's used all year long--frankly that's her prerogative, especially with so little of the year left.
I do think it's great that DH is working with your child and though it might need ramping back, and shouldn't be so test-focused, I would keep working with him for shorter periods. A lot of parents say kids must sink or swim on their own, but children are not born knowing how to study, or how to set priorities. A lot of parents just put kids at a table and say "Now, study for that test" but never demonstrate for kids how to break down material, figure out what's most important, think ahead about what would be good replies to questions, and so on. You are setting that foundation with your son and that's good. Just don't let second grade social studies and science turn into a fight at home or with the teacher.
If DH is really very frustrated, I would try to give him a break if you can, and take over the oversight of homework and studying for a while. There is just no reason for this to be about "blowing up" over second grade stuff. Each teacher is different and maybe you got one this year who operates in a way that's not the most effective for your son. But that's going to happen some years. And it might help to figure out how your son learns best; not all teachers are going to accommodate that, but you and DH will be better able to work with him.