If you have room for it, you could use a toddler fence to keep the dogs at a distance. I wouldn't put too much faith in it though until you're confident about its effectiveness with your dogs. The one at Amazon.com: North States Superyard Xt Play Yard: Baby has six panels that can be configured in different ways.

Oh, but just because they don't really need you doesn't mean they cannot learn to enjoy being with you. My lovies, except for a lone bachelor (and I am on the lookout for a girlfriend for him), are all in bonded pairs and loose in a birdroom so, if they didn't want to, they don't have to have anything to do with me but they come and perch on my hands, fingers and arms when I clean the canaries cages (the tops of the cages and the spaces in between are their chosen roosting spots) and beg for seed (which, of course, I give them as a small treat). It is better when they don't need you. It is as nature intended and that means a healthier and happier life for them. It is real hard not to be selfish with birds because we love them and want them to love only us but we need to be fair to them and give them the best life we can.