Hi kikithomps - you have a lovely backyard! I'd use pots in groupings near the corners of your stone walls and wherever dogs and kids don't run to bring in some color. I would stick with one bright color for the pots, preferrably a color you think you could find for many years to come in the stores. I love cobalt blue glazed pottery, but any brightly colored pots would work. Vary the heights and shapes if you like. You can really go wild with the plants since you get a good amount of sun. I like the chartreuse sweet potato vine, purple fountain grasses, geraniums, etc. Play with what you find at the nursery.
I would also add some flowering shrubs and trees to your back fence line as it looks like it gets good sun. Putting them there should keep leaves out of the pool and away from your youngest's shovel of death. Asking at your local nursery is your best bet for suggestions of flowering trees. Good luck!

Lots of potential in your backyard. A landscape designer would be able to come up with a plan that works for you. I agree with doing everygreens and flowering shrubs that don't attract incests and animals. Sometimes a garden looks quite interesting with shades of greens and yellows, adding some boulders create textures and character.

I would probably suggest keeping to containers near your pool and back patio area. I'm sure you spend the majority of your time there. Depending on your budget try to buy as large of a container(s) as you can. Maybe 3 containers on each side of the pool.

There are so many choices for containers now...(I agree...time to retire the whiskey barrel!) There are fibreglass containers that are frost proof and are super lightweight and come in many differents "looks" - terra cotta, copper look, black, stone. You could choose terra cotta....but make sure it's frost proof or in your winter they might crack. It costs more to get quality containers but it's worth it in the long run. There are cement containers with different finishes as well. I would suggest going with something simple but maybe in a terracotta finish to keep the same colour tone as your pavers.

The added height of plants in containers should keep your dogs from destroying the flowers/and or shrubs. If you have irrigation in your garden you can get them to add drip lines to your containers so all you have to do is fertilize once every week to 10 days. Putting a slow growing conifer in the centre will keep something in the container year round and then plant around it with seasonal colour. Tulips in the spring, annuals or perennials in the summer, and in fall you can put cut branches like cedar or pine for winter interest.

I hope this helps!