It is good to hear from you! I was wondering how you were going.
Yes, the funeral will throw you back a step or two. Once it is all over, I think you will feel a lot better. I don't know why, but when my dad died, I felt a lot better after the funeral. It was like a weight was lifted off my shoulders. Hopefully you will feel, and experience the same relief.
Life for you and the children will be different. You will miss him, but with time, things will get back to a new normal. As you said, "day by day"; baby steps.
I hope you are getting some professional help? This is all to much for one person to deal with.
Stay in touch if you want to vent.
Sometimes it helps to just put your thoughts down on paper or the computer screen.