Starting with the most difficult case, the anti-gun spouse, expect to walk an emotional tightrope for awhile. But since you love each other and are committed to working things out, there's reason for optimism. You'll get through this conflict just as you've gotten through others.
Let's discuss the concept of boundaries. In short, boundaries mean that you get to decide what you do, while he gets to decide what he does. You can choose to be armed or unarmed. He can choose to go with you or not go with you. He doesn't get to "make" you disarm, and you don't get to "make" him go with you. Your actions are yours and his actions are his. He cannot later blame you for going somewhere without him if you chose to go armed and he refused to accompany you, because staying home would be his choice. You cannot blame him later if you choose to make him happy by leaving the firearm at home and then something untoward happens, because you chose to go unarmed. You entirely own every choice within your boundary—and that includes any fallout that happens as a result of those choices.
Put differently, you don't need anyone else's permission to carry, not even your husband's. You don't need his permission to own personal property, whether it's a firearm or anything else. However, because you love him, you might find that some part of you needs him to approve of the choices you make. That's where things get tricky, but try to keep the distinction between permission and approval very clear in both your mind and his. You can bargain for his approval (and you often will), but he has no moral right to either grant or deny permission.
A lot of folks have found that just quietly doing what they do, without fuss and without making a big deal out of it, gradually lays their partner's fears to rest. As time goes on, the other person eventually realizes that you're not doing anything except going through life just as you were before. However, if you choose to make a visible power struggle out of it, talking endlessly, badgering him to "agree" to "let" you do stuff rather than simply doing what you do and letting him choose how to react, the conflict can last for years and become quite nasty.
Your husband needs to see that you are committed to safety and that you intend to keep your firearms out of the hands of people who should not have them. If you don't already own a safe, get one. If you can't afford a safe, purchase some cable locks and find a secure place to hide the locked firearms when they are not in use. Make security a visibly high priority and don't ever skimp on it. Whenever possible, enlist his help. Have him help you choose a location for the safe, or research safe types. Ask him whether he believes the not-in-use firearms are better stored in Place A or Place B with their cable locks in place. Discuss how you intend to manage your children's safety education as it relates to firearms. Ask for his feedback on such matters, listening to his worries and nondefensively accepting his concerns as the valuable data points they are.