First question.....why don't you send her the money to cover the rent so she doesn't need welfare?.....that part seems sensible to me.
Second question.....you will probably be stopped at the Airport...you will probably be stopped at Customs.....if you are very, very lucky you will get through. But why a one way ticket?....if you are intending to return back to the UK...work to support your wife and family during the PR process.....it would have been cheaper to fly return?
Are you intending to stay in Canada?....if so...you will not have health care...you will be unable to work...your PR application will take at least 5 months Outland and up to 18months Inland. During that period, your wife will have to support you and given that she is short of money, this put an extra burden on her finances. You may get lucky, get a job, a LMO and a work visa but still that takes time and probably happen within the same time frame as an Outland PR application.
So.....my advice would have been.....work in the UK....send in the Outland application...support your wife for the few months needed by not buying airline tickets......get your PR....come to Canada....but that advice is redundant now.....
So instead....good luck....