I have used an app called Screens Connect for this for a couple of years now and am very pleased with it. It comes with a service you install on the Mac side that keeps track of your computer regardless of NAT settings and other fun things like that. It was not cheap or free, but it’s been bulletproof and I am willing to pay for that when work is involved.
I feel your pain. I won a free iPad, and my frustration using it is one of the reasons I have stuck with Android phones, and not tried an iPhone. I love my Mac book pro, by the way, and am by no means an Apple-hater. But every time I use the iPad I get frustrated.
My advice is that Google is quite helpful. A gazillion people use the iPad, and a lot of them had whatever problem you are having. Someone already answered your question on the internet.
(That’s how I got my iPad out of “jiggle mode”.)