DH and I live 2.5 hours from our main family (and some are well scattered beyond that).
DD was in creche near the office and commuted with us daily, and we mostly managed it all between the 2 of us - her illnesses, our work panics, even DH getting knocked off his bike after dropping her off on her 2nd last day in creche before going to primary school. We just did a lot of juggling - working into the evening (long before WFH was a thing), arranging diaries when we could to get around travel committments etc. DD often came into the office with me at the end of the workday when creche was closing so I could finish off something urgent and I had a box of colouring pencils and bundle of colouring sheets in my drawer for her. (Original boss used to bring her DC into the office after school to do homework so turned blind eye, later boss wasn't happy but also didn't give flexibilty that he was supposed to so I just told him it had to happen or the work couldn't get done).
When we got to primary school, we put her into afterschool club near school (and home), but our 2 neighbours were also emergency contacts there which was useful a very small handful of times (about 4 times over 8 years when I was really late). And I also had a older DAunt who lived relatively close who minded DD once when DD was sick - but mostly DH and I had juggled like before. I managed to get into a car-pooling arrangement for 3 years when 1 afterschool sport moved from school pitch to a local secondary school pitch, so I collected 3 DCs at 4pm once every 3 weeks and gave the other 2 snacks until they were collected from ours, and I could collect DD the other 2 weeks from the other 2 houses. But everything else was in school or the afterschool club (initially a local creche that collected from school, later an afterschool on school site).
Normally, if DD was sick, one of us would start very early and do a long morning (6.30/7am to 1.30pm), we would meet at lunchtime to swop (in town near office if DD was well enough for the drive in the car, but at home if DD really needed to stay home), the other would do long afternoon (1.30pm to 7pm or so), and both of us would catch up a bit in the evening once DD was in bed. We organised our diaries to have our meetings on opposite ends of the day. Person at home was mostly on childcare/household chores, but could do some work while DD napped. So if DD was off for 3-5 days, we usually managed by just doing a lot of juggling and taking a very small amount of leave when it was really needed.
WFH really wasn't a thing at the time, so we were using our own devices not work devices for computers, we did both have work phones, but I tended to do a lot on paper when at home. Meetings were only in person in the office. But we could mostly make it work.
DD is now midway through secondary school. But Dh and I have always been a team on the household front.
And things like laundry, cooking, getting out the door and managing the house....take routine and being generally organised. So we try and do a wash every day while we're out, hang it out or tumble it when we get home, but then put the clothes into a clean hamper to fold at the weekend while watching a movie together. We have a lot of clothes so we are not under pressure to wash and rewear the same things during the week (a full set of 6 shirts, 3 full pe kits, spare jumper etc for school uniform; I have a lot of plain tops in different colours that I make exciting with jackets or scarves etc). I try to organise dinner for tomorrow night while I am washing up tonight after dinner (taking things from freezer, peeling/chopping/soaking veg to just turn on when you get in, etc). So when I get in from work, I just turn on pots, check mail, empty bags and find out about the day. When I am clearing up to go to bed, I leave everything out for breakfast and have bags repacked to leave in the morning, and lunches made in the fridge to put in bags in the morning.
It's hard, but do-able.