Hi ChilliPepperPlant and congratulations on the PhD. I think that the answers to your questions will depend on what subject area your PhD is in (you may not want to say exactly, of course, but loosely Arts or Sciences might make a difference) and also on where you see yourself ending up work-wise (i.e. are you aiming for a job in a research-intensive university or happy to do more teaching and less research in a post-92 institution?).
Just so you know where I am coming from, I am in my (very) early 40s with two dds who are 6 and 7. I am a Senior Lecturer and Head of Department in a small department in the Arts Faculty of a Russell Group University. (God, that sounds poncey... sorry... just so you know how relevant or not my experience is to your own.)
I have never ever seen an academic job advertised as a p-t post. However, my understanding of the relevant legislation is that if you got the job and then asked to work part-time the institution would be obliged at least to consider it and would have to have a VERY good reason for turning you down. We currently have a post-doctoral research fellow who is works part-time, but it has been easier for her because she doesn't have teaching and admin duties to fit in.
I did consider working part-time temporarily after I had dd2. However, I realised that my department (not where I am working now) would simply rearrange my teaching so that it was all on 3 days, would reduce my admin load slightly, but would basically expect me to continue as normal in the days when I was officially 'there', and then instead of having at least one day per week for research, I'd have no time for research, the same workload as before and half the money. At that point, I decided to go back full-time. Actually I did also consider changing to a teaching-only contract (because I wasn't confident of being able to fit in any research around a heavy teaching/admin load and two young children) but I was advised that that would basically be 'career death', so I decided not to.
So, basically I have worked full-time throughout the time my dds have been small. I went back to work after 18 weeks maternity leave both times, though I did manage to extend it a bit by timing my births carefully and using the summer vacation as extra leave! Dh didn't have a proper job till after dd2 was born (he was a PhD student and then was doing bits of part-time work) so it was essential for me to go back quite early in order to pay the mortgage.
If you decide to wait until you're ready to work f-t, I think that there are various issues to consider. I don't think that age is a major issue. Apart from being illegal to discriminate on the grounds of age, my experience is that departments genuinely want the best person for the job, regardless of age. However, you'd need to consider the gap on your CV between finishing the PhD and applying for f-t jobs. It's not that people will discriminate against you as such for having had a 'career break'. That would again be illegal. But it's that you'll be competing against people who've had time to gain more teaching experience and to publish between finishing the PhD and applying for whatever job it is. So, if you decide to wait, it would be a good idea to consider how to use the intervening period to make yourself as attractive as possible job-wise. This, in my field, would mean concentrating on getting stuff published. I'd think about publishing the thesis as a book or series of articles, but also about preparing to move into a new research area - which might be an extension of or development from the thesis - to show that you're thinking about the future. You could also gain teaching experience by doing hourly paid work if it's available. Again, this may depend on subject area, but in my area there's always a need for p-t teachers. You could 'manage' this, so that you did, say, a couple of hours a week, but only on a Monday, so that you wouldn't need to leave your dc for too long. If this looks feasible, I'd be looking for experience of giving the odd lecture (even if it's just one or two as part of a course managed by someone else) as well as seminars or other small-group classes. You want to show a potential employer that you are capable of teaching at all levels and in all formats that are relevant to your discipline (which may involve lab work or whatever... but science is a closed book to me!).
In answer to your time-management question. Yes, it is possible to have a certain amount of autonomy over one's time as an academic. That doesn't reduce the amount of work to be done, but it does mean that you can decide when to do it. I have one day/week when I work from home, even in term time (excepting occasional meetings... but I am HoD and go to more meetings - for my sins! - than I did when I was a Lecturer!). On that day, I don't have childcare and I try always to pick my dds up from school myself. I rarely work during the day at weekends (which I used to do all the time before I had kids). However, I work most evenings. My situation is particularly odd, as dh works shifts and often doesn't get home till about 9.30 p.m. We always try to eat together (otherwise days can go by without us actually speaking!) so that means that I usually work in the evenings between about 9.30 and midnight or 10.30 and 1.00 a.m. I am rarely in bed before 1.00!
I am not as research intensive as I'd like to be, and my research output definitely suffered after I had my dds. However, that was taken into account (somewhat!) by the last RAE (I submitted 3 items rather than 4) and hopefully will be in whatever replaces it. (HEFCE's latest on the REF does mention various equal opportunities issues. It's rather vague, but then the whole document is vague, so I'm not necessarily holding that against it!). Also, the facts that (a) I moved jobs when dd2 was 18 months old, and therefore had a whole lot of new teaching etc to prepare, and (b) have taken on a management role, have exacerbated the research situation. I could have made life easier for myself!
OK... I've written an essay, and I now have a student waiting to see me, so I will stop there. Hope this is helpful. Sorry it's so long. Get back to me if you have any more questions. Oh, and good luck!