Get thee to a training class!
At the moment you are reinforcing this behaviour - every time a dog approaches you haul back on the lead, push her down, hold her tight and force her to sit and squirm while a strange dog comes past, stress stress stress everywhere, no wonder she barks and goes for oncoming dogs if that is the result.
A good trainer will be able to teach you how to get - and keep - her attention and then gradually ramp up the levels of distraction until you're able to do it around other dogs. 'Watch me' is the key - rewarding the dog for focusing on you.
You can start this at home now, get whatever she likes best (high value food, chicken, cheese, sausages, a squeaky ball, anything they will obsess over), wave it at her, when she knows you've got it bring it to your eye level and say 'watch me'. If she tracks the object up to your eyes, a proper squeaky good giiiiiiiirllll! and she gets the treat. Repeat ad nauseum. You want the dog to focus on your every move and regard you as the source of amazing things.
Once you've got this you can start to add in other things - 'watch me - sit - stay - come!' etc., anything you can do to prolong the time that your dog is paying attention to you, even if it's a daft thing like 'paw' or 'speak', if your dog is watching you and waiting for a command that's perfect. It's at this point that you'd start to take this work outside and start working with other dogs at a good distance away, gradually working closer and closer. Many trainers will have a non-reactive stooge dog available for this purpose.
Poodles are very, very intelligent dogs and need a challenge like this to keep their brain ticking over, it's all very well doing two walks a day (are they long enough and challenging enough?) but you need to stimulate the brain as well and tire them out mentally.