I have a feeling the "raised under foot" expression does not necessarily mean índoors. I can see kids and puppies, kittens or whatever is being raised tottering in and out of open doors.
I like the underfoot expression better than domesticated because it is visualising the scene.
And sorry to bother with analogies again. We have a similar expression: "voor de voeten lopen" To hinder someone by being in front of someone's feet. Used like Jackie explained it.