Can you determine the reason your dogs dig up new plantings. Is it because the soil is easier to dig in? In my experience dogs dig during hot weather to get to cooler, wetter soil. I don't know why they would dig right now. You may have to do with your dogs what I have to do with deer. Fence off new plantings until they get established. Deer seem drawn to new plantings, even deer resistant varieties. I have no idea why, but once something is established it is safe unless we have a drought.

I use welded wire fence because it's stiffer and somewhat self-supporting. I tie the fence to the t-posts with twine because the setup is temporary, so the fence can be reused. The t-post are the hardest to pull up; it's a leverage thing my DH figured out.

The point is: dig up the bed, plant, and surround with fencing. Try this along your existing fence as you may be able to tie the protective fence directly to the existing fence. Landscape staples can prevent your dogs from nosing under the fence.

I recommend you use shrubs as they tend to be more difficult to dislodge. I can't tell if it was a cloudy day when you took your photos or if your yard is mostly shady. It seems fairly bright nonetheless, and even part shade shrubs should grow OK. Here is a list of 30 Shrubs for Shade, and here is another with 44 Shrubs for Shade. These lists have something for most areas of the U.S. Research any you like further to make sure plants will grow in your climate and soil. Also, do a search for "shrubs for shade in your state or city" to see what comes up. Visit a local nursery for specific recommendations from people who know the local climate and soils.

The area next to your steps could have low arching plants in between the lights. People always take the shortest path if they can. The plants should discourage people from stepping off where you don't want them to. This is a site where you have to make sure plants won't grow taller than you want or, especially, wider than you want. If a shrub will eventually be 5' wide don't plant it closer than 3' to a fence, wall or path. Remember that "dwarf" only means smaller than the species.

Is the wall in the upper middle and left in the first photo? I would plant shrubs in front of the lowest part of the wall between the two lamp posts to direct traffic to the opening there. This informal hedge might also hide the compost pile.

Right now you have lots of flowering trees, but you should choose shrubs for flowers, fruit or fall color later in the season. If your live in a southern state a lot of broadleaf shrubs can be semi-evergreen—keeping all or most leaves unless the winter is severe. If you live in a northern state, evergreens are most likely to be coniferous. Here is a list of small and medium sized shade tolerant conifers.

Put in a bunch of perennials and train the dogs to stay away.