^ can you cite specific Canadian law for this?
Under Canada’s Immigration and Refugee Protection Act (IRPA), if you have committed or been convicted of a crime, you may not be allowed to enter Canada. In other words, you may be "criminally inadmissible."
This includes both minor and serious crimes, such as theft, assault, manslaughter, dangerous driving and driving while under the influence of drugs or alcohol. For a list of criminal offences in Canada, consult the Canadian Criminal Code.
Individual rehabilitation
Rehabilitation means that you lead a stable life and that you are not likely to commit new crimes.
If you are not eligible to be deemed rehabilitated you must apply for individual rehabilitation to enter Canada. To apply, at least five years must have passed since you completed all your criminal sentences (this includes probation). You must submit an application to the Canadian visa office in your area and pay a processing fee. You should also check the visa office website to see if they have any special requirements.
Note: Applications for rehabilitation can take over a year to process, so make sure you plan far enough in advance.
So you may be allowed in with a criminal conviction but you would have to apply in advance for the "individual rehabilitation". I don't know how that is, whether they grant that readily or it's tough to obtain.
This is all off of the Citizenship and Immigration Canada website.
But I've been watching this new reality show they have on TV about the Canadian Border Services Agency at airports and land crossings and there are several instances on there where you see someone being denied entry because they have a drinking and driving conviction.