If your question involves those choices you made up and some of the issues, I believe:
Mexico is violent (I posted the CJ stats). We need border security involving walls in some places, but mostly some comprehensive border and immigration acts. Asylum seekers that don't meet criteria for deportation can stay in Mexico if they are safe until their immigration hearing. As a country we need to follow the rule of law regarding asylum seekers. (see Ninth Circuit decision specifics) Congress needs to pass new immigration policies that recognize their rights, preserve our sovereignty and their obligations under our laws, while facilitating trans-border commerce. We need to protect our citizens from the criminal element in Latin America (states and local government each have their priorities, sometimes differing). I would end "chain migration". DACA was established by executive order, and that needs to be addressed by Congress, who has abrogated their duty to act for the common good on immigration. Even if all the refugees have experienced "credible threats" we should not have to provide all with admission to the U.S. and with all the privileges and benefits citizens have. Immigration is by definition temporary, unless someone wants to obtain citizenship. I'd give the "dreamers", for instance, that choice. If the "Remain in Mexico" policy works for all sides and passes judicial review and oversight, I am in favor of it. If we can legally have a quota system for asylum seekers, I would favor that. These issues that Congress needs to address are clear. I cannot disregard the moral aspects and believe Catholic Social Teaching on Immigration is sound.
Catholic Social Teaching on Immigration and the Movement of Peoples
That may not encompass everything, but does it answer your question?
In short, I think there is violence everywhere unfortunately. I don't think a wall is necessary everywhere either assuming there are other ways to successfully monitor and IF (huge if) laws are fixed and enforced.
As far as asylum is concerned, I think 95+% of asylum requests are BS, and are simply economic in nature. We need to have honest conversations about asylum, as it's obvious that our system is getting completely abused and taken advantage of. If we can't set, and manage a clear definition and threshold for asylum, we're opening our doors to the majority of the world outside of N America, W Europe, and a few other countries/areas.
Back to violence.... out of the top 100 most violent cities in the world, the US has several. I believe I already posted the stats on several, and a good portion of those had heavy/dense illegal populations. Illegals, and those once legal aren't settling in safe areas, so it's very easy to question their true motive.
On Mexico. As a country their homicide rate is 4x ours. Much, much higher in border towns, and especially along TX. So I have zero problem with a big tall wall along most of that area.
Conversely, the least violent areas in Mexico are S Mexico, and interior Mexico. Just as safe, or even more safe than many states in the US. And VERY close to the Triangle countries. So again, points to economic motive.
Personally, I've spent a good amount of time in El Paso, and have friends that have lived there since the early 90s, and also friends in/from Juarez. I've personally lived and worked in Central America in the 7th most violent country (Belize) in the world with is 7+x our rate. I've had to bribe, grease palms, and I've seen the violence. Not all, but a good amount of the violence that goes on there comes from illegals from the Triangle countries.
In terms of the Triangle countries.... They are failed nations. Corruption and violence are ingrained in the culture. Something drastic will have to happen for those countries to self correct. Simply giving them money does absolutely nothing. At some point in time, the people will need to take it upon themselves to make change. Folks leaving in droves, only makes the economic situation worse, and strengthens the illegal and violent elements.
Even Belize, where I felt safe (I knew where not to go, and/or when not to go) for the most part, would slide into Triangle like status if it weren't for the ties to the UK. It has already slid plenty as Britain has slowly pulled away in different aspects. I personally got to see the UK close down several bases and pull troops. The increase in violence was almost instantaneous. I'm friends with the president's son, and the stories I can tell are simply insane. His father is retiring in 2020 after 12 years, and the party is picking the new candidate this month. From what I gathered, he wants to get the hell out even though he's cited health as a reason. In short, the problems in CA are growing outward. I'd bet the homicide rate in BZ grows steadily along with illegal immigration over the next 10 years.
In my heart, I'd love to give a pass to DACA kids. BUT... it sets a very bad precedent and encourages additional illegal immigration. I think the wall in exchange for DACA was a good bargain. Regardless, we need to close the birth tourism loop hole as it's simply too big of a carrot.
Big wall, big door, common sense laws and enforcement... void of politics...
PS... I'm sure there's many Catholic teachings you disagree with (as do I), so cherry picking what you like or don't like on an issue won't sway many folks. Just food for thought. There's only a few folks on here like Whiskey that I know walk the entire walk (or at least most of it) and can make that kind of argument an invoke the Church's teaching.