I am a Canadian chartered accountant planning to get work in the U.S. on a TN-1 Visa. However, I first wish to travel to my desired work location to try and find work. Is this permissible under a B-1 Visa?

The law is not absolutely clear on this issue but I believe the answer is most likely "yes". In general, even looking for work is considered entering the local employment market and therefore not within the scope of a visitor visa. However, there is a specific "B-1 in lieu of H-1" exception in s. 214.2(b) of the INS Operations Instructions which permits persons who would normally qualify for H-1 (CA's would be considered H-1B level workers) to enter as B-1 visitors provided that they receive no salary or other remuneration from a United States source. The specific exception does not exactly contemplate a professional entering for the purpose of finding a job. However, Canadian ports of entry are admitting business visitors on this basis.

If you seek entry under B-1 for the purpose of seeking employment, expect detailed questioning from the inspecting INS officer. Be prepared to show that you have the necessary professional qualifications to be considered an "H-1 level worker". It is best if you have definite plans (such as previously scheduled job interviews) rather than a vague intention to look for work.

Alternatively, you can always choose to go on vacation under a B-2. If you happen to find a job while in the United States on vacation, there is nothing wrong with that. However, if you choose to enter under B-2 you should state your primary purpose of taking a vacation rather than searching for a job.

I am in the US on a TN visa and have teenage children who would like to get entry-level part time work. How can they do this under the TD category?

They can't work under TD status. If your children seek part time work, they must qualify on their own for a separate visa. If they are going to school, they may wish to change status to F-1 which should allow them to work on-campus. Off-campus work authorization is permitted under certain conditions as well. There is also an H-2B category which may be an option, although it is difficult to obtain because a temporary labor certification is required. You may wish to schedule a formal consultation if you wish to pursue the matter.