I don't think you can have more than one doggie follower at a time unless you're on PC and have a mod for it.
I'm trying out a mod that lets you adopt Meeko and tell him where his new home is, i.e, you can "assign" him to any of the player homes that you already own. Just picked him up as a follower and told him he lives in Windhelm now. If I tell him to go home he *should* go straight to Hjerim instead of back to his shack. But we are on our way back there anyhow, so I'm keeping him with me for now. I will need to make a few stops along the way but no dungeons unless something unexpected happens. As far as having him on the road, I'm only level 23 or so on this character so the random enemies are nothing he hasn't been able to handle. Even with two other human followers who tank into everything just like he does, he is doing fine... I just have to make sure *I* don't accidentally do something stupid that takes him down, but so far so good.
Once we get back to Windhelm, assuming the mod works as promised, he'll no longer be a road warrior but just a very spoiled and privileged dog about town. Now I just need a mod that will let me put a little doggie Stormcloak sweater on him.
