You are in a catch 22. Public schools are the only schools that are legally required to follow any guidlines whatsoever for children with special needs; a private school has no obligation to recognize or accomodate ADHD. You could find a private school who did serve children with special needs, but this will be even more expensive than a typical private school is.
If you were in public school, I could tell you what to do for each of your children. While it is tricky, and some districts will be imposible to navigate, there are strategies that you can use to get twice exceptional children appropriate serivices, even if they are only accomodations for weaknesses and behavioral interventions. You would probably need the help of a skilled, possitve Special Edcuation Advocate to get what your kids need. Many public schools count on you not being able to get through the red tape and going elsewhere, however, with skilled help, you can make schools see the advantages of having IDEA elebile children who pass state mandated evaluations with high marks, it helps them in the long run.
My suggestion to you is to seek out the appropriate private therapy that will help them both be successful. If the visual issues are not run of the mill accuity issues (and I am assuming you are refering to visual motor, visual processing, and occular motor issues) then she would bennefit from OT and vision therapy. Cognative behavioral therapy would be a good addition for your daughter to learn some impulse control so that she no longer calls out in class. In a private school, they would also be under no obligation to cut a child with Tourette any slack either, not so in a public school, but in public school, children are served according to need, not diagnosis, so she would be accomodated even though her need was more commonly seen from kids who have tourrett, the diagnosis (or lable) really does not matter in terms of the IEP. Weekly cognative behavioral therapy will be essential for almost every child with ADHD. If she is not being managed by a psychiatrist, you may want to consider medical intervention. Once you are seeking theraputic interventions, having one more tool to help the therapy more effective, is very often the key to effective and long lasting progress. An inablity to suppress impulse is a common ADHD issue, and is one very specfic issue that responds to medical intervention with theraputic intervention very well.
As for your son, if he is not in speech therapy, I would seek some out. CAPD is very responsive to Linda Mood Bell methods, so if you can find a speech therapist who does these, you could help him significantly. There are other methods for sure, but this one comes to mind.
Here is my take on public schools: children do not fall through cracks, they fall through fingers. You can accomplish a great deal by advocacy, if the conditions are workable at your school district. Not knowing about yours, I can't say, some are unworkable. www.wrightslaw.com is a great place to learn about what to do, and you can find help from advocates on their yellowpages for your state.
M.