I've lead dozens upon dozens of beginner trips. Had to deal with the "suddenly" claustrophobic to the "now you tell me!" and the "gradual build up, I didn't realize that I was" types.
Claustrophobia is a fear that starts in the mind, it takes time and effort and a couple of other little tricks to overcome it. For would be cavers, Barbara is right... you got to WANT to go not HAVE to go. Having to go is doing so reluctantly and nothing you do will make that fear go away or even dissipate just enough for you to try and enjoy what you're doing. Wanting to go is your willingness and desire on a positive bent. But that little fear still creeps in and if allowed will run amok til it paralyzes you.
Study a bit of geology. Get an idea of how strong that "soft limestone" really is. Realize that it took millions of years for some of the passages you're in to form. Look at the passages you're in, solid and they're not going anywhere. They're not moving in closer to you. If they're 7-9 inches wide when you go in they're going to be 7-9 inches wide when you go out. They'll be 7-9 inches the next time you go in, even if it's 20 years later.
Keep busy, get your mind off where you are at the moment. Survey projects help keep the mind focused on the instruments and readings. Doing clean up projects get you looking for the elusive bits of trash here and there, or scrubbing the graffiti off the walls... which are usually found in BIG passages
. If you can get in, you can get out, simple as that. Been caving for over 30 years and gotten stuck maybe three times and I'm here at my computer writing about it. And no, I didn't go caving once every 10 years and got stuck each time.
Pay attention to the pretties that you see and admire them, realizing that you're one of a relative few to have seen them.
Your husband should be more understanding I think. Picking and choosing the caves you both visit with care. Do they have large passages with little or no crawls? No narrow slot canyons? There are caves like that usually in every state that has caves. Go visit them for short periods and extend the length of time each time you go. Gradually build your way up to it... or IN to it.
One lady I went caving with, turned out to be severely claustrophobic. We were doing a bat count for the NPS in a closed cave. Her husband and another ranger were in the lead of a 1000+ foot long twisty and sometime tight crawl. He asked his wife and I to hang back a bit while he and his buddy went to check on some other lead. We sat there for a bit then I noticed tale-tell signs of increasing nervousness. Glancing at the walls and trying to see everywhere at once, humming to herself, breathing just a bit faster... Hmm... ohh kay... "Hey Cristy, tell me something... how can you tell bat guano from rat?" She gives me a weird look and then explains... "interesting... also another thing I wondered... do mother bats always leave their babies on the walls when they go out to forage or do they take their babies with them?" 10 minutes later I learned a lot about the maternity care bats receive from a very animated bat expert. 5 minutes after that her husband called to us to catch up. Wish I had a camera to catch the look on her face as she realized what I was doing.
Taking your mind off the situation goes a long way. Keep moving in those tight passages will keep your mind focused on getting through there and what body part to move next.
And yeah... you don't HAVE to go underground to be a caver.