Hi, Thank you for writing.

Pines like soil that is a bit acidic, so dog pee (acidic) will not be a problem for them. I suggest ordinary bark mulch (not cypress), undyed (not toxic).  Sometimes over time, it can absorb the odors of the urine and then is easy to rake up and remove.  Don't use peagravel--it wanders. Don't use cocoa mulch--toxic.
As for plantings, Azaleas and rhododendrons can be toxic. https://plantaddicts.com/are-azaleas-poisonous/  There are a huge range of plants that are toxic to dogs. Many of these grow well under pine trees, so check before you allow a decorative plant to take over.  https://www.aspca.org/pet-care/animal-poison-control/dogs-plant-list

Although a list like the one above can drive you crazy--dogs do not like eating poison.  Having had dogs and cats and a garden filled with various toxic plants that migrated in from who knows where, my pets occasionally get nauseated and then I find the culprit and eradicate it.

Finally, just because your dogs are doing poop on your property, you still should pick it up.  Dog poo gets into urban groundwater and is a huge problem. https://smea.uw.edu/currents/scoop-the-poop-its-your-environmental-doody-pun-intended/

To answer that I would need a photograph of the trees and a note about direction. (Sun shade matters).
In general heavy peeing is tough for plants (see pee spots on lawns).
You might also consider some kind of raised container or bed under the pines but as of now, I have no idea of the dimensions or siting.