Mechanically...
In order to attempt to pin an opponent, they must first be on the ground, or perhaps pressed flat up against a solid surface like a wall. In order to put them there, you'll need to Shove them, requiring an Athletics Check on your part, opposed by an Athletics or Acrobatics check on their part (allows for Forced Movement to press them into the wall, or to knock them prone).
At that point, you need to place the immovable rod in an appropriate location to actually pin them to the ground. As I'll get to below, this is more complicated than it sounds. What this takes is going to be up to your DM, to place the rod in the 'right place' while your opponent is probably trying to prevent you from doing so. Personally, I'd call it a grapple check, either at Disadvantage for how precise you have to be in placing the rod, or requiring you to 'Pin' them (with the Grappler Feat). That's another Action.
Now you have to activate the Immovable Rod...that's a third Action.
And you have to do all of this without your opponent being able to break free.
(Realistically, it would probably require Grapple > Shove > Grapple again [to get the rod settled right] > Activate Rod...as this would allow you to sequentially keep them contained in a way so they couldn't just stand up after you knocked them down) So, a total of up to 3 to 4 Actions, depending on if your opponent is going to get a turn between you knocking them down and you working to pin them with the rod.
You can trim these down with class features...
A Fighter is probably your best choice here. Their multi-attack allows you to Shove and Grapple sequentially (PHB 195), then either take another grapple at Disadvantage (if you have Multiattack 2) and pop your Action Surge to activate the rod...or use your Action Surge to Pin, and wait til next round to activate the rod.
Why is this so hard?
Just for a reference on this: I have several years training with the short staff (3-foot). So this difficulty is rooted in my knowledge of how to use a staff to pin someone down.
In order to pin someone with an Immovable Rod, you have to place it in such a way that they cannot simply wiggle out from under it. So if your rod is poorly placed, if it is placed at an angle to their body (and not secured by another part of their body), or if you don't press it down hard enough against them--they'll just wiggle out from underneath it and be free. You describe it as being a 'very heavy weight.' But the rod on them will only press them down as hard as you, personally, can press it into them and still have a hand ready to press the button. And trying to do this while they are trying to resist you.
Most staff locks depend on the human holding the staff being able to tighten the lock to inflict increasing pain if the pinned opponent tries to get free. And they depend on being able to adjust the position of the staff to secure the lock if the opponent begins to attempt to wiggle free. Alternately, you can use a hand to grip the 'loose' part of the lock (often the wrist) to assist the staff-pin. This becomes necessary because a thin straight rod pressing down on the wrist is easier to get loose from than a hand that is wrapped entirely around that wrist.
While an Immovable Rod takes a DC 30 Strength check to move, it's not actually pressing down on you. It's simply stuck in place. So if you can shift any part of yourself so that the rod is against a thinner profile of your body, it's no longer pressing as hard. If it it placed against your chest, and you manage to wiggle to where it would now be placed over your stomach...it's possibly not even touching you any more. Once you set it, you can't adjust it to maintain the lock.
Even a 'pin' such as pressing the staff into an opponent's throat is more about the threat of 'if you move, I'll press harder' than it is about actually restraining them.
Furthermore, In accordance with this question, we can estimate that an immovable rod is only 2 to 3 feet long and about an inch thick. So given its length, you have to position your opponent in such a way that they can't reach the button. This either means standing the rod on end (which is very easy to wiggle out of), or making sure their arms are positioned in a way where they can't reach the ends of the rod effectively, either because their hands are restrained as well, or they simply can't reach it).
They may not know how it works...but the button on an immovable rod isn't exactly hidden. Someone grabbing at the rod might simply find it by accident.
What wouldn't work
If you try to simply lay it across their chest and activate it, their arms are free (your chest is thicker than your arms, and the rod is a straight object). And the chest compresses fairly well...you can wiggle out from something pressed against your chest unless it is set extremely tight. And if the rod is tilted at all...it'll be even easier.
If you place the tip into their throat and activate it, they may still be able to reach the button and either you have it pressed hard enough into their throat that they can't breathe, or they could just slip out from under it. And, well...placing it precisely there while they are trying to get away from you is not easy.
Similarly, pinning individual hands, feet, etc. simply won't work for these same reasons
What you need to do
For an ideal pin with an immovable rod, you want your opponent to be face-down, and you want to get them into a joint lock that can be maintained by the rod itself, and prevents the arm nearest the button from being able to move.
The simplest lock to use for this would be a hammerlock, modified for a staff.
So, start with something like this:
With the arm twisted up behind the back, then shove the rod through the bend in their elbow, pull their wrist as far up their spine as possible, and press the top of the rod into their wrist as hard as you can....then press the button. They might still be able to wiggle out of that...getting their hand out from under the rod, but it would be hard.
Best Answer
Thorn Whip normally cannot be used this way, due to its duration.
From what you described, the player character cast thorn whip to grab an enemy by the neck, and used gravity and a branch to hoist up their opponent, all while holding on to the whip.
However, as written, thorn whip has an instantaneous duration, which means there is no "holding on" to the spell. Once the whip has pulled the creature, the spell ends. The spell does not last long enough to strangle a creature or to be used as a climbing rope.
Going by the written rules, what should have happened was as follows:
As the other answers point out, you have discretion as DM over how things work in your games, so you can certainly allow creative use of spells and other features. Flexibility is generally an asset for DMs. Although be mindful with these rulings, as too much flexibility with the rules could eventually lead to issues with game balance or other disagreements between players.