LRD, it is not so much about the physical proximity of your supervisor, but that in the sciences, you have a physical requirement to be in a laboratory in order to carry out your research. Even if you are not physically in a laboratory, you will probably be using specialist computer software to analyse the results of your experiments, so will need to be located in a specialist computer lab. Your potential locations to carry out your research are therefore limited and there is an expectation that you will be busy in the lab every day. Further, the supervisor must ensure that adequate training and safety procedures are in place that whilst you are in the lab, you are not injured. Therefore, no student is ever allowed to work in the lab alone, they must always, as a minimum, have a "buddy" with them who can raise an alarm if something should go wrong.
Further, in the sciences, unlike the humanities, as a PhD student you will usually be working in a small corner of your supervisors field, which he/she will be established in. As a student, you are basically an apprentice and the degree of your independence will increase as you go through the process, with a supervisor and/or peers training you closely in the first year, through to you being able to defend your thesis at the end. I always said students were ready to submit when they were prepared to argue with me about their research and could convince me that they were right!
All-in-all though, regardless of the physical location of your research, the original comment made by the OP was that by doing a PhD, she was going to have the time to really be there for her children, which was something that she missed whilst working full time. She was expecting to be able to drop her children off at school and collect them in the afternoon. I still believe, if you expect that taking on a PhD allows a SAHM lifestyle with a bit of reading between 9am-3pm whilst the kids are at school, it is unrealistic. Anyone starting out with an unrealistic expectation of what a PhD is like, or how much work it entails is going to get a rude awakening and will either (possibly resentfully) step up to it, or drop out. IME, most will drop out which is a waste of student time, supervisor time and university and government resources (particularly if research council funded). Further, if research council funded, a student who does not finish on time, or who drops out will negatively affect the supervisors ability to gain research council funding in the future, therefore ultimately affecting promotion prospects for supervisors. Independence can therefore be something of an illusion and very much dependent on the individual student and their ability. If a student is progressing as expected, he/she is likely to be allowed to get on with it, with just monthly progress meetings, if a student is not making sufficient progress, that is a different matter.
P.S. Apologies if that doesn't make much sense - very tired this morning from working till late last night and writing this whilst procrastinating over an (over-due) book chapter - you see, it doesn't stop!