There are so many factors and history that cause this situation that it's hard to cover all points in answer. And you raise good points,.

The law is perverse, and the legislators that passed it are as accountable of this situation (democrats and republicans the same.. it does not have any logic, at the end, these people make laws that are very bad for USA and american society). IMO, this is a nazi-style policy, that makes USA look very bad and do a terrible thing. One case is separating children from parents involved in violent crimes or that put children in some real danger, but the families coming through the border come together and separation only make things worst. And I know that the separation happens for 'legal' people as well, and in this is also bad in lots of cases putting children at risk (but lets leave this point for another thread)

The asylum seekers can't really get to the port of entry from the reports and interviews I've seen, and even when they do, they face many issues. There is some reason for them to try to get in illegally. The system is actually perverse, not giving real alternatives for people in need.

But again, Trump had the option and he went for the worst.

The illegal immigration problem is very tough. Things have been done so badly for decades. And the US, unfortunately, is very accountable for its horrendous foreign policy and interventionism in Latin America, that broke so many countries, creating bad living conditions and forcing people flee to survive (not all fault of USA of course, but accountability is very high).

Parents will send their kids alone only if they are desperate (of course, there are sick people everywhere that want to get rid or whatever). But the point is that if living conditions were reasonable, a lot more people would stay. In some countries, kids as young as 9-10 get recruited by the gangs and drug lords as soldiers. Parents will do almost anything to save them. Even risking their kids to get raped on the long way to the US border, just hoping for a better future. And here we catch them and put them in a cage, managed by a private company that makes money by having prisoners (another huge stupidity, but lets leave the private jail business for another thread..).

It'll be very hard to come up with a solution, but nothing inhuman and violent will achieve something positive. Part of the solution is helping other countries to develop real democracies and improve their economies, making up for the damage done. Hint: dropping bombs, building more military basis there, giving away free taxpayer money that will be used by the local oligarchy, and the like , won't help. People will prefer to stay if living conditions were decent, rather than getting illegally into another country. Most immigrants rather stay in their land with families and friends, this is probably true everywhere. There is no perfect solution, but if we had policies that are respectful to all people, it would be much better. Then we have millions of undocumented people in the country, some of them spending most of their lives here. Most are very hard working that contributing to the economy, producing more than they take. They should be given an option to stay, and keep contributing (it's an opportunity, in lots of countries the birth rates are lower and they won't be able to support their social security systems). Did you ever talk to somebody that crossed the border illegally and told you what they had to endure? These people are very strong, and can contribute a lot. Of course, it can't be a free lunch for all, but this is the hard part (still probably simpler to fix, cheaper and more productive than so many other things )_