I like Aela in the home she's in (Markarth) and I am considering my Falkreath home as a second marital home. What I am thinking is to making my Dawnstar hold home into an orphanage. I have a housecarl, the female Imperial soldier from Windhelm's East Empire Company as my steward and a female bard. I'm sure they are capable of giving them a good home without Aela having to be there.

Is this possible? Also can you have children in different homes?

I have moved my housecarl out of my Markarth home so he could join the Blades (the real reason is Didn't want some other man sitting around the misses all day while I'm out saving the world).
That means I have a bed spare. Can I then move a child into this home?

Just ideas

You can only have two children, and only in the family home, so your characters wife will be with them. You cannot move children into the town homes without putting in a child's room. I would recommend saving before trying anything like that, who knows what you will lose.

So can I update a city house such as Markarth or Whiterun? If so how do this work?

I would think you go back to the steward you brought the upgrades from for that house, or whichever steward is around now, there should be an option for adding/changing things for your bigger family. you have stuff stored or on display in that areas you will lose it though.

The barrel under the Breezehome stairs goes with the alchemy room apparently, which you lose for a childs room. I have no idea what they do to Vlindrel Hall. I like my old houses as they are.

It's a lovely thought, though.

Just think of it this way: Constance's flyers are probably all over Skyrim. Maybe the Dragonborn isn't the only person with room in his home/heart for a lonely youngster.