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I believe that if you prune them back, then they will quickly regain control, and likely become harder to control. I would recommend digging everything out, completely. Some of this may be able to be done with a shovel, but you may find yourself needing some heavy equipment. You will have to contact someone in your country that can remove shrubs for anything that you can't remove yourself.

It is difficult to offer suggestions without a photo and more information. Some splitting of tree bark occurs from frost cracks or drying, some are structural defects that allow splitting apart of two co-dominant stems. Some are so severe that they cannot be saved, some are repairable.
Assuming that you have a mimosa tree with co-dominant stems that have started to split apart under over-burdened weight of foliage and rainwater load: you may be able to prevent further splitting by pruning both sides to reduce weight and wind resistance. In combination with pruning for weight reduction, you can install a cable support between the two sides. If it's a large tree this may be best done by a tree service.
Sometimes we bolt the two split sides together through the split, again it should be done in combination with pruning and cabling. There is no way to weld the two split surfaces together, just holding them from further splitting is the best you can hope for.

It looks to be a juniper hedge. If I'm correct, then I'm not optimistic about returning it to its former glory. Juniper does not break new stems on old wood that has stopped producing leaves. Trimming junipers (and many other hedge plants) with shears results in dense growth at the tip of branches which blocks sunlight to the interior. Without sunlight, those interior branches die. Creating some openings for light is crucial which means pruning, not just tip shearing

We did not receive any images and we would need the type of shrubs that you are having issues with.

No matter how you go about this, there is hardly an easy option. Invasive trees are very hard to get rid of, and are usually blacklisted. Unfortunately, they still make their way into unwanted places.

These two articles will give you a good starting point to getting rid of this pest tree: https://www.gardeningknowhow.com/ornamental/trees/tgen/weed-trees.htm

https://www.gardeningknowhow.com/ornamental/trees/tgen/how-to-kill-a-tree-killing-trees-in-your-garden.htm

Can you include a photo? This will help me to see what you are referring to.