Hate to ask this, but did you include a bed (maybe a closet/drawer)? Otherwise, not sure.
If you have adopted, you need to have the beds and required furniture for the children as well, their mum goes no where without the kiddies.
If you are on the PC, it could be a mod problem, mods for spouses, followers and homes can interfere with Hearthfire. Hearthfire also might not work with a spouse added by a mod.
What platform are you playing on, whom has your character married and where are they living currently? if they are currently a follower have you tried dismissing them.
Maybe she just wants you to furnish it a bit more?
Did you try moving to Ysolda's house, assuming you are currently living in Breezehome. Or moving to any other vanilla house you own then moving to Heljarchen Hall.
It seems you built the bedroom wing, do you have all three beds in that room as well as the children's chests. Have you adopted yet?
Give it a little more time. Wait 3 in-game days to see if things change. Sometimes, the game takes a while before it recognizes the house.
When I built Lakeview Manor, I had the same issue with Lydia. Then, one day, out of the blue, she says "This is a nice house. It could really use someone to take care of it. I'd be willing to do this."
I wasn't married to her, but she requested to be steward.
It was the first time I had seen the game do this, so hopefully this is what you're experiencing.
Try building Lakeview Manor and see if she likes that one.
Odd.
What quests have you done with Ysolda? She's got two: mammoth tusks and tree sap buying (this one is unmarked).
Hmm. Did a little cross checking on Google and Ysolda seems to be one finicky girl, and I think I know why.
Ysolda is also part of a radiant quest of buying tree sap. I don't think this should cause a glitch, but it's possible since now the game's expecting you to contact her about the tree sap.
Maybe try initiating this quest for her. Sleeping Tree Camp is west of Whiteun. Just follow the road, you'll run right into it. Take the sap from the tree, and talk to her about it. She'll tell you if you find anymore, to sell it back to her.
Exit the conversation when she says this, then talk to her in the evening, inside Breezehome. Maybe the option will show up.
If this doesn't work, try adopting a kid and send the kid to HH.
The last option may be to build another house and see if it helps trigger the option.
If none of these work, then I'd say your current game suffered the Bethesda Curse.
Side note: I did find an interesting post - someone said the time inside the new house may make a difference, and now that I think about this, it makes sense. When Lydia asked me about the house, it was because I started using it as my house. If this is a possibility, it may be worth trying.
Good luck.
I had the same exact problem with camilla and two kids. Was living at breezehome with them happily for some time, made the lakeview manor and assumed I could ask them to move but no such luck. Definitely had all the rooms set up and everything. This playthrough I'm doing now I'm not gonna buy breezehome, just build my manor then get married/adopt. I assume that will work fine.