Hugs, mama. I have lots of those days too, especially feeling like as soon as I feed everyone, the first one done is ready for the next meal. My kids are nearly 9, 6, 3.5; we have set up a routine where they know I will glady prepare 3-4 meals a day, but only once, so if you miss the 'it's time for a meal' call (miss, as in ignore, too busy playing) the plate will sit out for a half hour or so, or you make something yourself. We have lots of snacks available, they can grab fruit or a granola bar in between. I usually save dishes and most cleanup other than clearing the table/counter for once a day, at night.
I agree that it helps to get out. When my kids a play outside/excerise during the day, they are more willing to sit and read/be read to afterwards. Do you have a routine where you can get out in the morning, then come back at/after lunch? Can you read aloud to your kids while nursing the baby? Or set them up with a project to work on while your take care of the youngest?
I find that throwing in a surprise day every once in a while helps us break out of a rut and adjust our routine - like either a big outing, or just something minor like doing schoolwork outside, or switching around the order in which we do things, or coming up with a new way to make a list or schedule of things to do.