I've been HE my DD age 6 for about 6 months now, and have DS age 4 and DD2 age 1 as well.
We manage because DS goes to kindergarten (nursery) 2 days a week, and on those days, when the baby naps, we get a lot done - just really knuckle down and do all our 'busy' work which ticks my mental boxes, and then I feel I can take a more relaxed approach for the rest of the week.
Can you find a way of carving out some time to cover what you see as the 'essentials', so that you can feel more confident and chill out a bit the rest of the time?
As for autonomous being easier to manage - well I'm not sure I agree (obviously different strokes for different folks though!).
I was really keen on being very child focussed and interest led (still am in theory!), but just found that with the little ones about I just never had the time to sit and chat with DD about what she'd like to do, and to facilitate lovely explorations of intersting things. I want to do it, but it just wasn't working for us, and my lofty ideals seemed to be all or nothing - and so we did nothing
So now I have writen myself a basic structure for a terms worth of work, day by day.
eg Monday: reading (new book), practice sight words, maths - revise fractions, read non fiction together.
I have also just picked a topic for each week (how things work, the sea, the body etc) and found a science experiment or a craft relating to the topic and schedueled that in.
This is working really well for us. I still have a lot of flexibility and can change plans or tailor things to suit DD's (and DS's) interests, but it saves me from having to think of something to do whilst wrangling a crying baby and trying to listen to DS's constant (lovely!) chatter as well. It also means that if we have a bad day and I really have no time to spend with DD one on one, I still have a few things up my sleeve to get her to do, and so at least feel as though we have covered the basics for the day.
I hope that helps - I always find reading about other people's HE helpful myself. I think it does take a while to settle into, and to find your own way of HEing.