Do you give her any money? (money talks)
Does she now want to see daughter at all? Seems very odd she would only want son and not daughter.
Since her laws are so backwards, be careful about going there with daughter as she can maybe get her courts to give custody to her too before you get to leave to come back.
Write your congressman, go see them. They sometimes can help in these situations using politics but both of you have custody depending on which country you look at.
Also, I would stop all communication through the school. You are playing into her games. Send school a letter that states she is not to communicate with daughter at school and her mother has free access to her after school by cell phone. She either calls daughter at your home/cell when you are there only. Your daughter should not have to deal with this at school. Maybe ask her to have her call daughter, you will hand daughter phone when you see her number, then put son son and your daughter will hand phone to you. No communication between the two of you. Can you use email for communication? What about skype? You have sole custody of your daughter so protect her from her craziness. Play her game a little. She can talk to daughter when son talks to you. It is not like you are going to get in trouble here, you have custody. If she starts craziness, hang up and let it go to voicemail. How often is she trying to communicate?
Send her emails at business like at you can:
ex
Teachers daughter called me about your email. There is no reason for xx to be dealing with this at school. You can free cell phone access to her after xx when she comes home. You called my home number on xx date at xx time when you know we are not home. From now on, xx will be available on every Saturday from xx to xx time for you phone calls and then I will speak to xx. Both of our kids should be able to be in each others lives. I miss xx just like you miss xx and we should work together so they both grow up knowing both of us.
You
(fill in skype times or whatever you do). Keep it very tight to times and days so you and your daughter are not dealing with her all week long and daughter knows every saturday she can talk to her).
and yes, here in the US, you can try to get order enforced in family court BUT needs many many times of proving they are not following court order for anything but a slap on the wrist and saying...let him see kids. The whole system in a complete mess and only works when parents want it to work. Sad...
Originally she asked me to pay
child support. Later she dropped her child support request (I think she hope she would have a better chance to win the custody by doing that). So, the answer is no.
Yes, I will be very careful when I visit the country. I will not take my daughter with me.
Yes, she wanted to see our daughter, but she doesn't like the
supervised visitation. She was being super nice to me for 2 months, and then she asked if I would allow her to visit her unsupervised. Of course I said no. I told her I would stick with court order (supervised visitation).
Thank you so much for your suggestion and the formal letter for the school. I really love your idea!

We tried to work out call and skype time during custody battle, she refused to cooperate. I provided plenty of time slots to accommodate time difference (14 hours diff). Since she kept rejecting, finally her lawyer picked the time on her behalf. But those only worked for 2 months.
After that she tried to call sporadically. Sometimes even pass my daughter bedtime. I reminded her via email, but she always disregards whatever I say. Very, very hard to ask for her cooperation.
Btw, I couldn't find the congress contact info for my district. I found a link, but the webpage had been removed. Do you know a good website?
Oh, I see....yes it's sad that the justice system regarding family law is a mess here....
May I ask for one more suggestion?
Currently she has direct access to our daughter education (because it's available online). Thus she can see her weekly progress: homework, grades,
report card. In the meantime, she claimed our son's school there doesn't have online system yet. Thus she scanned and sent only his report card to me, but only the last one.
I asked the school one time if they would remove her direct access, and I will forward my daughter's education information manually. But the school refused since she has been in the system. Can the school do that?
What happened if I move in the future? Can I possibly ask the new school to not add her? By doing this I hope I would get more bargaining power in her game.
As of why she only picked the son, all I know is that at that time, she couldn't persuade our daughter to go with her. My daughter has been much closer to me since she got addicted to Facebook games. My son was still very young back then, he was only 4. She managed to persuade him (I don't know how).
My theory is, she managed to use our son to get our daughter, because in her statement she sent to the court (and also during mediation) she kept emphasizing "what a terrible situation when siblings have to live apart."
My other theory, she did that to hurt me, because she told our son to use her last name (thus, remove my last name) on his skype account, etc. At school he still uses my last name.