Make them better, be a leader. I'm so tired of all of this I'm a great raid lead but I can't deal with player problems. No, you aren't a great leader you are a great strategist. You can assemble the correct strat and communicate it to the group that is about 1/3 of raid leading. The other 2/3 is getting your raiders on the same page, managing them, and inspiring them to be better.
What you need is someone who plays boomkin to talk to her on her level. Some people don't do research at all and when they do they get confused and frustrated. Someone showing her what to do as another boomy would probably change her tune. Really the only fight her dps is going to lead to your end is Blast Furnace on heroic everyone needs to pull weight there and even then it isn't that bad. Each member is different and the game is pretty easy so making someone better isn't very hard if you approach them correctly. Talk to her boyfriend, maybe she just plays because he plays and isn't really that interested in raiding. The best way to handle her is going to be ask what she wants out of raiding and then tell her to achieve that you and her need to get together and look at her rotation and movement. Is she using DBM? Is she paying attention while raiding? Have her download GTFO. DPS numbers don't matter all that much in Normal or Heroic. They make shit easier, but they don't make or break many fights. Maybe she is just awful at boomkin. The issue I imagine is that she just really isn't that into raiding.
Your shit tank is an easy fix. He's raid led, he understands messing up, and it sounds like he and the other tank don't communicate. They should know each others CDs and learn from each other. If he talks to other tank and realizes other tank only uses 1 cd for each breath he'll probably mimic that activity. He's just over panicking and blowing cds he doesn't need. He needs to have faith and trust in his healers. Let him know you've got his back. He's trying to compensate for his failures on his own. Make sure his gear is set up optimally (I'm sure it is, that is an oldschool problem) and let him know hey on those breathes just do one CD and I've got X healer on you solely for that breath don't worry if your health dips we got eyes on you. Make him feel like he can trust his heal team. Communication outside of Raid chat between healers and tanks makes a fight work. Healers should always coordinate CDs (as you know since its the fix that got you leader), and should communicate with the tanks personally through whispers or a separate channel. Keep communication open and ready. Flame breathes are killers on Bender, but so are a lot of other excess damage going into a breath. Your dps don't stack up right for a bomb and tanks each a massive chunk right before a breath and it becomes fatal. Etc.
Look to really raid lead you need to have a goal, all your players need to be on board with this goal, you have to deal with each raider on the individual level, passive aggressive talking in the shadows behavior isn't something you can do and have a healthy raid environment as a leader. You have to handle each person with kid gloves. People hate this because deep inside they don't want to lead. They want to lay out a plan and walk away and just assume its all going to work out and when it doesn't they just want to kick whom they see as a failure and who is the lowest on the buddy-buddy chart. A great leader can mold a player and lead them to water and get their asses to drink. But it all starts with each individual players goals. Also on Darmac just call the spears for a couple attempts and she'll probably start to pick it up. If she is apathetic then let her leave she might be happier not fucking with raiding. Your other tank I think just needs some confidence and trust boosts. Oh, I also removed my wife from a raid I led. Why and How? She couldn't perform and her interest in doing so was waning so I told her to quit and she was happier, she misses it sometimes but knows she doesn't have the interest in a scheduled raid environment. Make the players who are under performing understand that it isn't just them its a team effort and their lack of interest hurts the whole team. make the decision seem like theirs, because really it is. You can only do so much to make them better but if they aren't interested they'll never be better. Talk to her boyfriend maybe he knows something you don't. I'm going to assume they raid from the same location.