A DUI is a Criminal Code offence in Canada and admissibility is based on the equivalent crime in Canada. If your crime carries a prison sentence of 5 years or more in Canada, then you can't enter Canada at all. But for lesser crimes, there is a process to enter without issue. But you don't just show up at the border and expect them to turn a blind eye.
It works the same way going to the US, by the way. Any conviction and you are ineligible, but again there is a process to follow to be allowed entry, but it can't be done at the border itself. I'm not sure how anyone would expect any nation to offer an open border to criminals.
The big issue I see with regard to Mexico is that Mexico buys more US-made products than any other nation if you live in quite a few states. Wages in Mexico are roughly the same as China these days; the infrastructure doesn't support some manufacturing, such as electronics, which is why China still makes the majority of that category. Perhaps more to the point, it is unlikely that anyone posting in this forum doesn't own some PRC-manufactured item.
But if you want to buy a refrigerator or freezer, you can practically guarantee it was made in Mexico, as more than 90% of that product category is. And Mexico paid a huge price to sign on to NAFTA as it essentially destroyed their domestic corn industry. Virtually all the corn consumed in Mexico today comes from the US. In the last 20 years Mexico has increased it's purchase of US made goods by more than 300%. Mexico buys more US made goods than every other nation on Earth except Canada.
Trade is a two-way street. An import tariff on Mexican manufactured goods will almost certainly result in an import tariff in Mexico on US-made goods. I am not sure what the US will do with regard to Trump's stump promises ... the Republican Party is a Free Trade party, the Democrats are the Protectionists. It was Republicans who negotiated the Canada-US FTA (1988) which was the blueprint for NAFTA, and Bush instigated negotiations in 1990 and all three parties signed NAFTA in December 1992, adding Mexico to the trade pact.
So we have a US President who is at odds with his own party. He may not be able to implement anything in the end. My guess is he will try, fail, and blame others for that failure. But that is just a guess.