So basically, I have two children's bed's and they are both "owned".
When I go to the orphanage in Riften she keeps saying I have not met the requirements even thought I have two beds, a chest and a dresser.
I believe that my housecarl and steward has decided that the children's beds belong to them.... I'm not sure why the hell this happened because I have two single beds upstairs that are meant for them (they have even been sleeping in them... but they do not show as belonging to anyone) and I have two double beds as well.
Why did they take the children's beds and how can I get them back?

I assume you have the "bedrooms" wing built. Do you have both "child's chest" items in the bedrooms wing? Normally the two small beds and dresser in the upstairs portion of the main hall should be enough to adopt, but give that a try if you already haven't.

I have never seen anyone but children sleep in the children's beds, that is why they say they are owned, only children can sleep in them.

I have one child's chest, 2 child's beds, one double bed and 2 dressers in the Bedroom Wing. I read on one of the Skyrim wiki's that this was a bug, your steward and housecarl taking the beds making it impossible to adopt. But I even tried killing them to no avail. Today I'm going to build a dresser/chest for the upstairs beds then, hopefully that will work.. Thanks guys.

Having only 1 child's chest would rule that house out, each child's bed needs a chest, go put the other chest in if it is still an option available on the workbench. Once you put the bedroom wing in it makes no difference what you have upstairs, the children cannot use those beds. The main hall single beds are only used by children if there is no bedroom wing. Saying it makes it impossible to adopt just because you have a problem with one house is ridiculous, surely you have other houses. If you own all the houses and build the new ones stuffing up 1 out of 8 does not make it impossible to adopt. And if you can still put the missing child's chest in there should not be a problem with that house, at least not as far as adoption goes. if the chest refuses to show on the workbench, and you are determined to use that house for your family, you could go back to a previous save game and build the house again. Maybe building ALL the bedroom furniture would be an idea, instead of trying to cut costs.

The bedroom wing needs two child's beds and two child's chests. If you do not have the bedroom wing, you need two single beds upstairs and the dresser that goes in between. iI is possible a glitch occurs if you have the bedroom wing, and do those beds before you do the upstairs bedrooms, never do it that way.

Why are you making that assumption? It could be a new character, or maybe he only wanted the one house. My current character only owns Lakeview and no other homes.

Even if he only owns one house, there is always the option to buy or build more.

Yes, there is. But you seemed to already assume that he surely did have other houses just as you've also assumed he's "cutting costs." Some of us like to start new characters from time to time, and that could be his case. Building a Hearthfire home on a relatively new character, particularly if you're opting to farm most of the materials on your own is time-consuming. If bricknee hasn't got his home fully built yet then it's likely a sign that he lacks the resources at this juncture, not that he's cheap.

He's having an issue. Nice of you to throw out suggestions for him but do they need to come with a scolding?