I think it's good that your therapist is interested in helping you get in touch with your feelings. If you shut down the negative feelings it has a knock on effect with joy and excitement, and can make it really hard to be playful and things. It's not bad to ask your kids to express their feelings with words, that is a good thing. It's not bad that you aren't getting overwhelmed with tears around them either, but it's good to get in touch with your emotions, and be able to show them all your feelings!
It's really hard to unbottle stuff. I do think it's well worth doing. It helped me getting hypnotherapy, and doing self hypnosis. Also listening to Anna Thompson. I couldn't really connect with a therapist before that, and would keep going back to a kind of script. I listened to John Bradshaw's Homecoming recently, and that brought up a lot of emotion, especially anger.
I would guess that, if you are feeling lots of sadness and fear most of the time, you have deeply suppressed your anger and joy. It can be really scary to face up to anger that's been repressed, and sad to face up to joy that's been repressed too, so sometimes it's really got to get worse for it to get better.