You're right that there is no 'right' to immigrate across another country's border sans permission of said country. And you're right that both parties kicked the immigration can down the road---for different reasons.
Hillary didn't make herself clear because she wasn't going to do anything about it lol. Why would she want to? Mexican immigrants make virtually instant democrat voters. They come here looking for work [or trouble in many instances] and entitlements. And no one blames them. I'd do the same thing, probably.
Hillary's status quo. Trump is the change agent and Trump's electoral lift off was on account of his promise to build a wall.
Contrary to media myth/hysteria, there's no good reason it can't or shouldn't be built. Other countries have them and they've been around for millennia. From the immigration status quo perspective, the wall isn't like laws that can be passed with a wink and a nod, only to be ignored when the Law becomes inconvenient later on.
But a wall---is a wall lol. It can't be passed and then ignored like a law can. And yes, they aren't an absolute barrier, but it would cut the flow of immigrants from Mexico to a trickle, literally. It would also drive up the cost of drugs on the street, but that's how it goes.
The media consistently portrayed us Deplorables as rank xenophobes and bigots for merely wanting the country to enforce its own immigration laws. Like sane country's do.
Since they wouldn't, we gave them Trump, and the wall.
<----------Hillary Clinton