Hi Irene, I think you are doing the right things and Atex has given some great suggestions.
I have had tics most of my life and now dystonia, and I have kids with ADHD, ASD, and other issues. But now that I have figured out some genetic - environmental connections, we are all doing much better. Here's a few random thoughts:
1. Gut health (microbiome) issues is the most common cause of chronic health issues, including neuropsychiatric. Anaturopath or other integrative or functional medicine doc can do a test like GI-Map w/zonulin. Zonulin is to test for leaky gut, ie overabsorption of undigested proteins or metals, etc. If you can't find a doc in your area, Planet Naturopath may be able to do in US.
2. Unusually high levels of manganese (not to be confused with magnesium) can lead to under-pruning of synaptic circuits and excessive dopamine release especially in the basal ganglia This can result in someone who is hypersensitive to stimuli, odd coordination, high anxiety, tics, and has difficulty sleeping. On the positive side can lead to high intelligence or creativity. Thus genetics that predispose people to high manganese are not defects.
3. In order to keep manganese levels, gut issues, and immune system under control, it is important to:
Maintain vitamin D levels at what healthy people who spend all day in the sun produce. See "The Vitamin D Council" recommendations.
Avoid iron/iron stores deficiency: Iron + Ferritin testing can tell you. Like with D, testing is needed to avoid oversupplementation.
Ensure enough magnesium. Along with Iron and D, used to treat hyperkinetic conditions such as restless legs syndrome and tics.
Avoid manganese or other metal -containing air pollution. As Atex mentioned, cooking especially smoking oil in a saucepan messes up air. Reducing PM2.5 using true HEPA filters has helped change my life. Sources of high manganese include steel-working factories, auto body repair, welding, battery making, and train tracks if the wheels squeal (and shed). Less so are busy roads. For general PM2.5 AQI, check purpleair.com or other sites.
Manganese is usually best tested with Red Blood Cell manganese or trace minerals testing. If your daughter is at the higher end of the "within range" levels, it can still contribute to tics and auditory or visual hallucinations. But the things above can help the body bring back into a more normal range over time and also reduce immune system issues.
On a final note, I used to inject glutathione but much more effective is fresh broccoli or especially broccoli sprouts. This stimulates glutathione production in the cells where it is needed. Broq is a pill version that is fully reacted sulforaphane. It was effective for me, but it's expensive and contains copper so it's best to ask you naturopath.