I think that given my background I can give you some sound advice. I ride horses all the time, and while not IC, I still ride at times being diapered.
I understand what you are saying and have experienced the same problems you have described about diapers or pads being "torn apart" by the movement. I often am riding at many different levels, sometimes at a full gallop, or even just a fast trot, and the amount of movement will cause most disposable types of products to fall apart once they have become wet.
Because I am involved in not just riding for pleasure, but searching for cows --sometimes on precariously steep slopes or in thick brush and trees, the thought of having to worry if my diaper is going to leak or be noticed by others is not something I want or have time to do. Hence, I too need to have a method that really works.
As far as wearing plastic pants as extra protection, I have found that that is usually a must, as the movement tends to push liquid out of the diaper even if it is the most absorbent and high quality. There has to be something that will be a backup layer of protection.
What I think is indeed the most effective, comfortable, and least likely to cause an embarrassing experience is wearing a cloth diaper, such as an "all-in-one" that contains not only the absorbent material, but also an outer shell. The cloth material isn't going to break up, or bunch up, like disposable products do. While they are more expensive than disposables, I think you will find that they are worth purchasing, even if only during the period while you are riding.
Just to be safe, wearing a thin pair of plastic pants gives some added level of protection as well as confidence that you are not going to have a noticeable leak. The plastic pants do become more uncomfortable during the summer, but it is kind of a trade off.
The problem with cloth diapers, as I am sure you might know, is that when you need to change, it is more difficult as you are not just going to dispose of the diaper by throwing it away in the garbage. When on an extended ride, this can become a bit challenging, to say the least.
However, what I have found is that it is very possible to ride horses, even in the most extreme types of outings and not have to experience embarrassing leaks or uncomfortable circumstances. I have found that the extra padding of wearing a diaper actually can make the experience more comfortable with less chaffing and soreness than without.
Good luck in your riding experience. I love spending time on horseback, even if most of the time it is spent working rather than just having fun.