No option to move my child from house

Instead of moving her out, which will essentially make her a NPC townie, you may just want to buy another lot and build a simple house. Sims that inherit the Good Upbringing trait complete activities faster than your first generation Sims. Much faster.

If she doesn't have a three-star Good Upbringing because you aged her up before you should (sometimes the game will prompt you too soon, and if you have many children, it's hard to keep track of. You can check your child's progress with Good Upbringing if you go into a parent's contacts that shows everyone's traits. I think that there might be one star for each of baby, toddler, and child. The Sim I moved out of the house I had accidentally aged up too quickly. I regret not changing her DNA first, because now that she is a NPC townie, I can only change her clothing.

tap your family potrait, tap your daughter, and tap "Move Out" to move out your daughter.

I don't know but you could try clicking on the family portrait on your wall. Hth