Do you put your baby down for bed awake?

Usually, I nurse my daughter to sleep. I like doing it, and I know if (when) she wakes in the middle of the night, I can feed her for a min or two and she will go back to sleep.

What I dont like, is she is still walking 4+ times a night, and now sometimes staying up for a half hour. My husband is getting frustrated too because she wakes him up all night before he has to go to work since she in still in our room.

We've tried sleep training, which worked ok at first but then teething happened and now she just cries and cries until she works herself up. If my husband goes in to settle her she will freak out too, it has to be me.

Her doctor said she should be able to sleep through the night at this point, but I don't know what to do! My husband wants to put her in her own room but we tried that twice and it was even worse, and I hate hearing her cry. Any tips?