I feel your pain! I have spent the last two months doing all of this. I think that I gave Goodwill a whole store full of stuff, as many carloads as I took over. (Well, it feels like it!)
What I did was start in the bathrooms and dump everything that hasn't been used for a year. It's hard for me to do that. I try to use what I buy, but I don't always like what I think I'll like, so it's hard to get rid of it. But I was a bit ruthless. Then I moved to my kids' bedrooms, then other rooms. My bedroom was the hardest - especially my clothes. My husband's job was the garage. That was a lot of work and included selling some stuff out of that.
I have to admit that I had to make several passes, and I probably will do more. Giving up furniture, especially when it's part of a room design, is hardest for me. I took several rooms to family members and the furniture will stay with them until I decide if I want to take it back.
Planning to live in a smaller place is hard, but I look at it as "freeing" now that my kids are growing up. I have great memories from all my "stuff", but part of moving on to a new stage in life is allowing ourselves to let go of "things". I'm to the point now that I will soon be an empty nester, and I've made a decision to downsize as I become an empty nester to help make life easier.
It might not be the same for you, (you have smaller kids, I think). However, if you can look at this as a way to de-stress, rather than as a stress, it will help you.
Btw, I did try to use one of those websites that does furniture placement, but it was not helpful. Instead, I got thick stock grill paper where each block represents a foot, and cut out pieces of paper to represent my furniture. That way, I could determine the sizes of rooms and figure out which furniture would fit in each room. Maybe that would help you.
Good luck!
Dawn