Interesting thread. I am SAHM with a child of school age. I do voluntary work at ds's school two mornings a week, and visit my elderly Mum every day, which takes about an hour a day, by the time I have gone there and back. I spend most of the rest of the days doing housework, shopping, ironing, gardening etc. But I do find I have some spare time.
Obviously I don't have as much washing and ironing as the OP, as I only have one child, and I don't have a dog.
I think if you really have no spare time at all, then you are maybe not being very efficient in the use of your time. Sometimes I find I'm rushing to get things done, but it's usually because I've spent too long on MN not been organised enough.
I can see how your evenings are busy now though, as your dcs are older. I tend to find I spend time with ds when he comes home, then cook, eat and clear up after dinner, then get ds to bed. This all happens a bit later these days as ds is older, so it leaves you with less evening. But I don't mind that too much. The benefits of being a SAHM for me are that when It gets to about 8.30 or so, my time is my own, rather than having to do cleaning/ironing etc in the evenings or at the weekends.
I think the only downside is that some days I feel life is just full of domestic chores. But if I worked, I would still have to do all the domestic chores, and find childcare for ds (and I'd rather have the time with him). And not be able to visit my Mum very easily. As we can manage on dh's money, it makes sense for me not to work at the moment.