$2k is not a lot but should be enough for a good life. An apartment can rent for about $600 USD a month (surely you can find cheaper or much more expensive).
If you can, I recommend living in Condesa.
Finally, if you are employed elsewhere i.e. not in Mexico, you can live indefinitely in Mexico and pay no local income taxes. Lots of foreigners do this.
I do have friends that feel like the safety is not good enough for raising kids, so there is that.
I think as long as you stick to safe areas, you should be fine.
Re: visa You can find the requirements here [0] (I don't know why it is in Canadian dollars).
I have a handful of Spanish friends that are under this visa. They technically work in the US or Spain but are "temporary residents" in Mexico. Mexico only requires you to pay taxes on income gained in Mexico. So if your employer (or your clients if you are a freelancer) are abroad and the proceeds are deposited to a foreign account, then Mexico does not tax that income.
[0] https://consulmex.sre.gob.mx/leamington/index.php/non-mexica...