Does your DD have additional needs or is it that she's angry about her dad not being around?
If it's additional needs, it sounds like you are doing your best to get her help, and that's all you can do really. Don't feel guilty about it not happening quickly enough, you're fighting for her, which is the important thing.
My younger DC has additional needs, and over the last couple of years I've had to arrange the diagnosis, numerous specialist support appointments (physio, OT, SALT, audiologist), apply for EHCP, apply for DLA, apply for specialist school plus school transport on my own. Despite only splitting with my EXDP a year ago, I had to do everything on my own as he was not interested/did not want to accept DC was struggling. I also had to apply for CMS once EXDP made it clear he was only going to pay £300 in maintenance for 2 DC (when he earns £60k). I'm also hopefully completing on our new home this month, after my last attempt at property buying fell through after 7 months.
It can feel overwhelming at times when you've got lots going on and it's just you, and you've got to be mum, dad, good cop, bad cop, all rolled into one.
What helped me to limit the feeling of being overwhelmed was taking each item in turn; so I only applied for CMS when I'd exhausted all other options. As DC was coming up to start school, I applied for EHCP and DLA one after the other, then schools and transport following.
It may also be that your DD needs more support with managing her emotions. Are you able to talk to her on a one to one basis, or do you have other DC vying for your attention? My older DC who has no additional needs find it hard that younger DC gets more help due to their diagnoses. Are you perhaps able to take DD out for their favourite treat and let them know it's ok to feel angry sometimes, and that you love them, are supporting them etc?
Sorry if I'm wide off the mark with the above, there's not a lot of information about your situation in your OP (which is absolutely fine for your privacy), so I'm sharing from my own circumstances how I've dialled down on feeling the pressure.