The landmines in Afghanistan that killed the two girls are persistent landmines. They are alive perpetually and don't self-destruct within any time limit. As the report suggests, they are remnants of the Afghan-Soviet war and are now mostly in the hands of terrorist militant groups. These are the type of landmines that should be banned, and many responsible states who are not signatories to the Ottawa Treaty are phasing them out or have done so.
The anti-personnel landmines (APLs) that are used by many modern armies today are non-persistent and self-destruct within 120 days. And APLs are not the most destructive of weapons that maim or kill non-combatants, but integral in a military unit's defence, as the article in the link I posted above has shown.
Which makes the Ottawa Treaty a joke. It does not ban improvised explosive devices—an alternative version of APLs—or the more devastating anti-vehicle landmines, which maim and kill at far greater degree than APLs.
But a point of greater significance that makes the Ottawa Treaty a farce is the declaration made by several countries like Australia, Britain and Canada on the articles contained in it before becoming signatories:“It is the understanding of Australia (insert UK and Canada as well) that, in the context of operations, exercises or other military activity authorised by the United Nations or otherwise conducted in accordance with international law, the participation by the Australian Defence Force, or individual Australian citizens or residents, in such operations, exercises or other military activity conducted in combination with the armed forces of States not party to the Convention which engage in activity prohibited under the Convention would not, by itself, be considered to be in violation of the Convention.”
Australia went even further to declare much more where its military and citizens can benefit from the use of APLs from non-signatory states without running foul of the Treaty, and you can read them here: Ottawa Treaty
If Australia, Canada and the UK were truthful in their commitment to the Ottawa Treaty, they would not have included the declarations before their signatures. But why did they? The answer is obvious: UK and Canada are part of Nato, and Australia has a long-running defence pact with the United States, which has not signed the Treaty with good reason.
In any war where these countries are allied with the US or other non-Treaty states, they wanted to make sure they could operate without hindrance and this includes the benefits that APLs would bring them. Paint it however you want, it is insidious and hypocritical, especially when they pontificate over non-Treaty nations.
In reality, the Ottawa Treaty is a lot of hogwash, with self-righteous chest-thumping and back-slapping by signatories eager to boast they are leaders of the human rights cause. But there is no real policing to monitor that member countries live up to what the Treaty calls for. Nations that have signed and ratified it only need to declare they have emptied their arsenals of APLs and that's that. Already parties to the Treaty—Angola, Burundi, Ethiopia, Rwanda, Sudan, and Uganda—have used APLs with impunity after signing it.
Treaties are formulated and conducted between states, and not NGOs. Other non-Ottawa members like the US, Israel and Singapore (through Asean) are parties or entering the Convention for Certain Conventional Weapons, which is the right forum to eradicate the use of persistent APLs and other similar type weapons.
The Holy Father's exhortation that you provided must be seen in its proper context, in the larger picture of the Church's teachings on just war, the indiscriminate killing of non-combatants and the right of every country to defend itself against unjust aggressors. In this light it makes sense.