Mom2four I am sorry to hear about your daughters diagnosis.
I was diagnosed with polyarticular JIA myself when I was 8. (knees, wrists, fingers, hips and ankles)
I would like to reassure you about methotrexate, which I took from about 9 years-12 years old. Then later in life on and off. I was under care at GOSH and methotrexate was the absolute turning point in my treatment. Steroids were short lasting, naproxen helped a bit, but meothotrexate kicked the arthritis in the bum.
Your dd will likely have one or two blood tests a month to check liver function. The worst side effect I had was sickness. I hated taking methotrexate (For me it was a couple of tablets taken once per week) as it made me feel sick the day after. Doctors and family thought I was playing up, but it is now a known side effect of methotrexate.
There is the option of having a weekly injection if your dd does not like the tablets.
You say your daughter has mouth ulcers- poor thing, I know methotrexate can cause stomach ulcers (I am not medical so don't know if these two are linked? But perhaps something to bring up with the consultant?)
It takes 8 weeks for the MTX to 'kick in', once you start taking it so don't expect immediate results. I have a friend who it didn't work for, but he is an adult.
I really hope you are coping well and your daughter improves soon.