Hi.
First of all, I'm going to give you a big virtual hug. I've been there, and it is hell.
Secondly, it's hard not to, but try to keep some hope. Until you have a specific diagnosis, it's impossible to know what the future holds. Mass doesn't necessarily mean tumour, and tumour doesn't necessarily mean she'll die. I know it seems hopeless and you dare not hope, but the path ahead will become clearer in time, and it may not be as bad as you think. But the waiting is awful, I get that.
Thirdly, WTF are the hospital playing at. It might be they know something which means that don't need to rush her in, but they need to talk you through things properly and give you support. My 2yo had surgery on her brain tumour in under 24hrs from diagnosis, after being blue lighted from our local to the 'big: hospital. It might be due to the location it is in, and it's size (sounds huge but relatively little), posting little immediate risk, and features on the scan which make them think they don't need to rush her in. It might be they think it's something other than a tumour.
So how they are acting is alien to me, but I'm assuming there's reason behind it. This isn't really something you can go private on though. I'm not sure the facility exists in the UK for private pediatric neurosurgery (where treatment is needed, it's usually very prompt so no need, and a private hospital wouldn't have the facilities). You'd also be taking about hundreds of thousands of pounds I suspect.
Can you phone up your local hospital and ask to be talked through timescales etc, what exactly they've found, why is safe to leave it etc?
Would you be comfortable saying which hospital you'll be under? If not, that's fine.
Ps: we are now 10m into this journey. It's low grade, which is as good as you can get with brain tumors, but still terrifying.
Good luck