I'm generally pro-immigration, but you're right and make valid points. I'm a UK citizen but we face similar problems in nature if not magnitude. My position is that controlled, proportionate immigration is good for the country (UK, but generally too) both culturally and economically and should follow legal due process.
My main criticizm of the Trump administration's handling of the situation, as an outside observer, is that they are persistently and maliciously bypassing due process (muslim ban imposed arbitrarily even on legal residents while people were in the air, separating children from their parents, etc). Frustration and revulsion at these actions naturally throws a sharp spotlight on whatever else the administration does with regard to immigration, and rightly so. As I said, you're probably right on those incidents, but it's also fair to say that the degree to which a tactic is used also matters, and they deserve every single bit of enhanced scrutiny they face on this issue.