You're correct, the root cause is never fixed. Let's focus on the cause. Illegal aliens is not the cause, but the effect. Just like our ancestors, they come here for the opportunity to live a better life than they had in their own countries. After all, that's what made America what it is. So, lets get down to brass tacks: what is the source? Business people that hire illegal aliens. Right now, if you run a business that is discovered to employ illegal aliens there are two possible consequences. FIrst, although I've not heard of this being done, you could lose your license to operate your business. Second, you could be fined for each employee and incident. FIrst incident,, $250-$2,000 per employee, Second incident, $2,000 to $5,000 per employee, and third incident, $3,000 to $10,000. If the Illegal alien problem is costing American taxpayers so much, then that cost should be shifted to the origin of the problem: businesses that hire illegals. To fund those programs, Increase the fines. FIrst offense, $10K, Second offense, $20K, third offense, $50K. These fines would PER employee. The current fines are nothing to an employer because he can make up for it with his slave wages. Make it so it hurts the business, and the practice will stop.
The second group of illegals coming across the border is the more troubling one. They're the ones that are fueling the drug problems. How to handle that? Follow the lead from Portugal that has eliminated the illegal drug trade by making drugs legal for recreational use. The dealers can't compete with the open market. Read up on how that's been working for them since the country implemented the legalization. We aren't talking about just pot: opioids are legal, too. amazingly, the drug abuse problem there has dropped because the funds once used to fight drug abuse has been channeled to treatment and rehab. Unlike the opioid crisis in the US, the drugs available there legally are not contaminated with fillers that affect the person's reaction.
If you want the problem fixed, you have to go to the root of it. Make it unprofitable for illegals to come here and we'll have extra funds to protect our country from other threats.
FWIW, when you asked who would pay for the Dreamers college, you are aware that they don't qualify for government assistance for college. No Pell Grants, no student loans, etc. Unless they acquire scholarships though foundations, schools, and even their churches, they have to pay for it out of pocket.