skybluish, I don't see how a lawyer is necessary. There is no legal argument here, she has the right to sole custody of the children and has the right to remove them from Taiwan.
Does she have passports for the children ? If so, then she can leave Taiwan with the children now. And if not, what is stopping her getting them ? She's a Taiwan citizen, she's and her children are all on the family register (and I don't see how her BIL can remove her without her permission), so if she has lost any documents then she should be able to obtain all of the necessary documents from the relevant government office.
The Bureau of Consular Affairs website
http://www.boca.gov.tw tells you what documents are required, I summarise here:
A completed passport application form
Birth certificates of children
The parents' marriage certificate
The ROC passport of
one of the two parents
Two identical passport photos of the baby (45x35 mm or 1.77x1.38 inches, color)
So there should be no problem at all for her, unless there is something else that you are not telling us ? By all means travel to Taiwan to give her support and help her with the kids on the flight. But there is no legal problem. The only thing she needs to worry about is the BIL trying something underhand; and as long as she takes care there then she will be fine. It's simply a matter of her getting the hell out of Taiwan with the children, as soon as possible.