Started to do someone's fence, she kept harassing and calling when we said due to weather we could'nt finish yet, we told her we are not continuing due to her constant calls, she gave 600 at the beginning for materials and labour, do we have to reinburse her and now she is threating to slander our company in the local town paper any advise?

First, you have a contract. A customer asking for the status of their job, however insistent, is not grounds for terminating that contract. If you decide you don't want her as a customer that is your right, but you need to refund what she paid.

Second, slander is spoken, libel is printed, If she complains to the newspaper about what you didn't do and she tells the truth, then you have no recourse. Its only if she lies that you can take legal action.

Also she came to our house banging on the door yelling in the neighborhood demanding to know what's happening after we have told her several times on the phone.she had RCMP come over and bylaw come over as well, this is turning into a mess, and since we put in the poles and there was some labour involved we feel she should not get her money back, she has since had someone else take out our poles and redo some work, but today called and threated to tell lies regarding our business in the town paper, and if we do owe her back money,how many days until she would be intitled to the refund? And should'nt we be intitled to some of that since we put in the time in the beginning of the job

Why don't you go over and finish the job, weather or not,

If someone else "finished" the job then the weather should have been good enough for you to have done it.

Sounds like you need to pay her back all the money and personally sounds like you need to provide better service and/or inform the customer on a regular basis of their status

Yes, if You can document work you did, you can deduct that from the refund. Though she may not like that.

You have to weigh whether its worth fighting a libel suit or losing the work you've done.

... but today called and threated to tell lies regarding our business in the town paper

Sounds like extortion to me.

I assume your are somewhere in Canada. The law there may be slightly different than in the U.S. but not completely.