Home education will require travel, likely more travel that involves you than a drop-off and pick up. All the trips, all the play dates, all the social activities, all the educational events require an adult to not only travel but to stay with the kids most of the time. I've spent years going all over the city, I know others who go much further to get the activities and to regularly meet up with friends.
Taking travel out of it or reducing it to where you can walk risks isolation and it is so easy to get isolated when you don't have to go out every day. I'm a disabled home educator and I think the idea the HE is naturally social ignores that the parents or another adult have to be social as well for it to work. When I've been hospitalized, when I've needed mobility devices which impacted how we could travel, when I've been unwell physically or emotionally, it impacts where my kids can go and do. My 7-year-old can't go to a HE group unless I do. My 9-year-old can't do 'home education group rock climbing' unless I am there. Most things require parents be on-site for legal reasons and the ones that don't often put in that you need to be either within a certain time-distance (my oldest's art club requires a parent to be within 20 minutes of the building while they are in there) or to be able to pick up at a moment's notice. Socially or academically, it's all on our shoulders.
There are isolated kids in schools, I was one of them, but it's important to know that without intentional effort that can be draining and overwhelming, it is far easier for home education kids to become isolated. This often given ideal that 'oh, my home educated kid plays with people of all ages' is a bit rosy-tinted when you see the reality of these groups which can be just as cliquey and vicious, when the parents of the little kids crow how great it is that your older kids will play with them when you know your kids would absolutely love more than anything to not be stuck between sitting out with the adults and playing with kids half their age when either there simply are no one else their age present or the few there are have rejected them. It's hard and it can be heartbreaking, I think that has far more to do with why so many older kids get out of the home education groups than qualifications. While we're frustratingly in an educational blackspot, it does give a lot more options than home educators and home educated kids are going to get.
Home education can be great, but like most great things it takes a lot of hard work and can involve a lot of dealing with tears, worries, heartbreak - your own and the kids. If you think home educating is going to solve your overwhelm problem, sadly I think you're in for a world of hurt. I would not pull out unless an emergency until you have an academic and social plan that is solid and you have your whole home backing this move because it will take everyone for it to go well. Put the rose-tinted 'I know it's going to be great' aside and really look at what all of your options are. I think finding a solution to your transport issue would do far more than taking all of this onto what reads like very stressed shoulders. HE does not solve stress, it just changes it.