Originally Posted by JALPak
chinese new year is jan 23rd not 19th
Yes, true. However, note that the Chinese start their New Year celebration and travels a few days before the actual new year ("Year 30, year 29..." for "day before new year, 2 days before new year, ...").
, I did a search on for your week of travel, and availability doesn't look too bad. If your family can take an overnight layover, you can take the next morning flight JL805 on Feb 2.
There is also good availability on CX's sole NRT-TPE flight, but it does depart early at 3:30 PM. You didn't say where your wife is originating, but if they can catch the early 9:35 AM DFW-NRT flight, they can connect to CX 451 on the same day.
A last option would be to look at upgrading the tickets to business class, as there is availability for NRT-TPE in business class almost every day.
[BA] NRT-TPE 2 x Y seats 01-30 + 5 days
TH-02-02: CX451, JL805
[BA] NRT-TPE 2 x J seats 01-30 + 5 days
TU-01-31: JL809, JL805
WE-02-01: CX451, JL809, JL805
TH-02-02: CX451, JL809, JL805
FR-02-03: CX451, JL809, JL805
SA-02-04: CX451, JL809, JL805