I got a letter saying I can transform my lab in Breezehome to childrens room. So I went to Whiterun and talked to the steward Brill and payed him 250 gold to transfrom my lab to a childrens room. He said next time you visit it will be furnished. But it did not happen. Its a bug.

It sounds like the very bug which makes the Lab uninstallable in Breezehome when Dawnguard is installed.
Hopefully some mods may be out for this one soon seeing as one is out already to fix the breezehome lab bug with Dawnguard.

I had this problem too. The option to buy the children's room was still in the steward's dialog even though I bought it over and over. First charging 250, then 500, then 250..... Eventually after about 4000 the room had changed to a child's room. But the option to buy it was still in is dialog and he still charges money for it. Definitely a bug.

And are you running any mods for Breezehome?

Just the house markers. Nothing else.

Same problem here. I'm only using the markers for Breezehome. I've paid him twice but still nothing.

Did you try temporarily removing Dawnguard? If it is the same problem as not being able to buy the alchemy table in the first place then doing that might fix it (just uncheck under the data files list before you play). You can reinstall Dawnguard once you have the furniture (or the alchemy table if run into trouble buying that).