Well the first place I would start is with their determination, their strategy. See, if they solve something like the border crisis, how are they going to polarize voters in upcoming elections?
And if the Democrats and Republicans wanted to "solve the border crisis", why didn't they?
So first they have to decide whether they WANT TO solve homelessness, income disparity, etc. Because if they do solve those things, what will they campaign on next time?
I think therein is the problem with the Federal US government, and why they need to get rid of Trump. They are afraid Trump will solve the problem, or get too close to solving it.
I would suggest solving the homeless problem is partially possible (I've been homeless and some of them don't want to stop being homeless).
Build the Wall.
Use adequate amounts of border Security through Law Enforcement.
--->The Illegal immigrants should then adopt the ways of more typical Americans after a time. Immigrant families will cease to populate a single apartment or house with so many friends / relatives so rent and mortgages (which encourage higher rates) should go down in price. <---
The Americans who are homeless could see that there is a more affordable way of life after --->the cost of living<--- goes down.
The Homeless will have hope to be able to support a better life for themselves.
But it would not be good just to give them money from the government, more than food stamps and child care.