Oh yes, sorry, I did skirt over the most important part there 
DS (now 6) was like this at 3 too and still is occasionally, he was today, I've got better at handling it but also he's got more mature. What I did today (restrained him safely until the issue to fight over was gone, screen banned him for hitting me, shut myself in a room rather than him in his and then talked to him sympathetically when he broke through to tears, which took me by surprise - he doesn't usually cry in a sad way, just angry).
I remember whispering brokenly at him in tears "HOW CAN I MAKE YOU DO STUFF WITHOUT SHOUTING. HOW CAN I WORD THINGS BETTER." While he just hummed away at me infuriatingly, pretending to swim across the kitchen floor, and one time I bumped into my next door neighbour on the way to take him to the childminder, late again, she innocently asked me how I was and I burst into tears on her and said "I can't make him get dressed or eat or leave the house on time and I am such a failure as a mother"
(She was lovely and totally lied about never hearing me shouting through the wall and said we've all been there and not to worry!)
If you're in a position to do so you can restrain while she calms down - position her body facing away from you, you sit down on the floor, hold her arms with your arms, but that doesn't work if she bites you and/or pushes down on the floor which is what DS used to do as his legs were stronger than my arms. Also might not be possible when your younger one gets more mobile.
If you have no option and they won't calm down and you can't separate any other way then you do have to put a closed door between you. But I know that can make some children panic. I don't know what you are supposed to do in that situation.
I did find that making the sanction no-cooperation-required did help because it reduced the kicking out against it. Yes DS would rage and/or cry about it when I said you're now banned from screens for the next 30 minutes but he'd get over it more quickly than I thought he would. If the tantrum is relatively non destructive like AnotherMonkey describes then yes leave her to it and wait until she's ready for a cuddle. Always give a cuddle. If it's violent or destructive then you have to try and get her to a place she can't cause any damage or do the restraint thing like I described.
Also remember - it's really not nice for kids to tantrum. They don't enjoy it, they don't do it on purpose to manipulate. When they're doing it it's because they feel like they have no other option, either because they don't know another way to deal with the situation, they don't feel heard/understood, they don't understand what you're expecting them to do, they feel scared or pushed into a corner. If you can work with her you can massively reduce the tantrums because you can help her see she has other options. Of course they will still happen - she's three - but hopefully they will be less frequent and less prolonged.
And don't worry if you and DH have different ideas and approaches. I was so scared of letting DH do things his way at times but sometimes DS responds a lot better to DH's way even when I don't think it was the right way to handle something. Let him try things - you can't expect him to take your methods seriously if you don't let him have his go too. The only exception would be if you felt he was doing something really counterproductive or something you're not in agreement with e.g. smacking. But talk to him - he's human and he gets it wrong like you will, we all do. Give him the benefit of the doubt and remember you're in it together and you try to support each other as much as you can.