I would ask them if it's alright to get to know their dogs so they will be comfortable seeing you in your yard. You know, the old "honey vs vinegar" thing. Unless the dogs are completely unsocialized, they should stop barking once they get to know you. Tell them you want to avoid "the other neighbors" complaining about the dogs barking at you, since you'll be outside gardening most of the time.
It's too bad they cut down plants without talking to you first(I would be in tears), but at least they're fencing their dogs in and not tethering them or letting them run loose. Good luck with this situation, it's a tough one.

I would just write off the plants. It was a bit rude that they didn't at least inform you the plants were too close to the property line to remain there when the fence went in. With a heads up beforehand you would have had an option to move them. Some people just aren't real comfortable socially though.

The dog thing is a real pain in the rear. I love dogs, but dogs that are allowed to bark constantly are a definite nuisance. One way or the other you will need to spend as much time with them as you can. Only once they accept you will they allow you on 'their' property and stop barking.

IF you aren't able to make nice with the neighbors for whatever reason and they won't control the dog barking and they aren't receptive to your socializing with them there is a technique a buddy used that worked for him. Some would consider it slightly less than ethical so it's a last resort kind of thing, but feeding the dogs over the fence makes friends fast in many cases. I say it is slightly unethical in that you are feeding someone else's dogs and they might not appreciate it. Still, a yummy piece of meat quickly trains the dogs to view you as a treat bringer. As soon as they view you as a treat bringer and not an invader they will likely stop barking at you. Once this happens you never have to feed or even look at them again. Their former view of you as an intruder is over.

Good luck.

Ditto on feeding the dogs.

Cheap hotdogs cut into small rounds will make fast friends.

Noinwi, I *was* in tears over the peonies. I'd moved them 3 years ago, so they were just about to bloom again (groan). The forsythia did need to be trimmed (I was putting it off because alot of birds nest in them), so I guess I'll just cut them down.

I've asked to meet their dogs, and if I could run them in the morning when I run my 2 labs (tired dogs are good dogs). But they've told me that they aren't yet socialized, and they weren't sure how they'd react to other dogs (the dogs are yearlings).

Justaguy...I think your 'unethical' technique is a great idea. I do have training treats for my guys. It might be a good idea to have a pocketful when I go out in the yard. I dread a summer of gardening with a couple of barking dogs.