OK, I will share--but first, know that my house should really be kept a bit more tidy and I am hs two children and I have a four year old too. So, things may be a bit different.
My OLDER child (5th grade--11yr in January) is a very independent learner. I set up her week in a portfolio on Sunday. There is a slot for each day. In it I put worksheets, assignments, or whatever will be helpful. I also put reminders (like empty dishwasher, or practice piano) in there. We start "school" at 9 and are usually done by lunch. However, she can stretch it out throughout the day if she likes. I just set aside the 9-12 part of my day for my "teaching". So, the mommy required parts need to happen at that time. She is using sequential spelling so we do that in the mornings. She is using Life of Fred for the most part and is independent right now (most is review right now) but if she has questions OR if I want her to demonstrate something, we do it in the morning. We discuss books together--well this happens anytime but often over breakfast or lunch. We are using Meet the Masters and do it Friday mornings.
Ideally, 12-3ish is for lunch and housework. However, life happens and we take opportunities when they are available. Also, there is one day that piano is at 1PM. The kids usually do their chores at this time and then play or create or self guided learning. Sometimes, my oldest will work ahead so she can have a day "off".
The reason mornings are our "school time" is two part. One, my 4 yr old goes to prek 3 mornings a week. Second, most random activities and scheduled things happen later in the day.
For you, I would look at nap times and designate those as "teacher" times. Most teaching would take place at that time. Your 6th grader can probably self initiate a bit and be or become pretty independent too. He can play with baby while you do some housework and he can contribute by doing chores too. I think you will be able to maintain an orderly home and still homeschool. Life will be different and there will be a transistion, but I think it will be good.
Good luck and enjoy.
amy