Every institutions policies are different in each of your situations above. I recommend going to your local credit union and talking to a loan rep. If not already a member, you would need to become one and open up a savings to apply/get a loan. Since you have the better credit you need to be the primary on the account and loan. Apply with your husband as coborrower so you can use his income. Most CU's price the rate off of the primary or higher scoring borrower regardless of who has the income. I've seen a lot of loans approved this way over the years. If they won't allow him to be on the loan due to his credit then you would typically need to apply with someone else as a coborrower w/enough income to qualify with debts on your credit report, their credit report, and the new car payment.
In regards to having your grandmother be a cosigner, at most institutions based on your situation you wouldn't qualify. A cosigner gives strength to an applicant but the primary borrower (you) need to have income and qualify for the payment amount on your own. No income means you wouldn't qualify. Typically the cosigner also needs to qualify for the new payments with their current debts. If they don't have enough income to support their bills and yours, then you/they wouldn't qualify. If they were to allow just you and your grandma, she would be on the loan as a cosigner and it would report on her credit report until its paid off. It could affect her future borrowing needs by having the new debt on her credit.
It is true that some insurers require all licensed/of age people living in the home be placed on the policy. Not all do so you will need to call around and ask questions. Also typically all people on title need to be on the insurance, again it depends on the insurance co. I have seen routinely where people have listed spouses or roomates as "excluded drivers" on their policy because they will never drive the vehicle. Check with your credit union to see if they allow this, if they do then you won't have a problem and you will be in compliance with their loan agreement.
Check with your credit union if both you and your husband need to be on the title if not, then just have the dealer put you on title. This will simplify the insurance portion and keep him from any liability on the vehicle.
One last note on not having him on the policy, DO NOT under ANY circumstances allow him to drive the vehicle. You never know what can happen that is out of your/his control. If their is an accident and he is driving the vehicle the insurance company WILL NOT cover any damages and you could end up with a huge suit against you from other parties AND you will still be stuck paying on a loan for a damaged vehicle.
If you have any more questions or need clarification, please let me know.