When she is pulling her head is up. i have tried to do the passive-agressive soft reins then strong half halt when she pulls but this just raises her head and she gets more worked up. i do lots of gridwork for her to get her on her haunches and to introduce her to larger jumps. Thanks everyone for their suggestions so far! this is a really helpful site 😀
I would keep something with the poll pressure, but would change to something that will work on the bars rather than an even distribution over the tongue. The bar pressure helps lift the head, tongue pressure brings the head down. So something with a nutcracker action, a small port or a very short link might help. Doing some grid work and raised poles will help too, to place her in a rhythm and sit her on her hind end rather than pulling down so as to try and train her out of it for long term. Hope this helps :)
This is probably going to sound stupid and counterproductive, but try not to constantly pull on her if she pulls on you. Only pull back if she gets really strong or if you feel like you need it, make sure it's a strong half halt. If you constantly pull on her or half half her, it's just going to become an annoyance that she will ignore. As for the rooting, every time she roots, no matter how fast you're going, make her stop and back her up a few steps. Get her on her haunches, then ask her to continue.
she is constantly pulling and sometimes roots after a jump
Maybe try a rubber or straight bar Pelham? I know lots of strong/heavy horses that go in those bits. Does she root or is she just constantly pulling on the bit?