Q.How can I get a burning bush to grow after dog’s pee?
I have 2 burning bushes – one is big and beautiful. The other is 1/3 the size of the other. Both planted at same time.
I take it you feel the dog's peeing on the one bush is the reason it is much smaller than the other one. While that may be a possibility, there are others, and you need to investigate these possibilities also. One very likely cause is that the smaller plant gets less light, or the soil or drainage in its spot is less beneficial. It might even be in a less protected spot, and thus suffer more from winter weather. Also, it smaller plant may have some disease or pest affecting it; you might take some leaf, branch, root, and soil samples to the nearest county extension office for their analysis. This link will help you find the nearest office:
This article might give you some more ideas: https://www.gardeningknowhow.com/ornamental/shrubs/burning-bush/burning-bush-care.htm
There's not much you can do about dog urine; a lot of water will probably do more toward washing it away than anything else. Perhaps this article about steps you can take to keeping unwanted doggies away will be useful. https://www.gardeningknowhow.com/plant-problems/pests/animals/keep-dog-out-of-garden.htm