My DH joined about 5 years ago (along with a fair few people in their 40's!)
He had to go away for training for about 6 months I think (you certainly wouldn't be able to do this part time)
We are about to have out 1st DC and I know that I can not rely on him AT ALL for child care etc. he never finishes on time (sometimes 6 hours late!) and his days are all over the place and not regular (how easy would the be to organise childcare?)
Also..... I don't know anyone that has gone into the job on a part time basis, however I know of a few that now work part time since joining which leave at certain times etc. because of this other officers have to take the strain I.e if a job comes in late, the part timer never takes it so the others have to knowing that they will be late home to their own families. (Slight resentment to these people)
I think its the kind of job where realistically they may not take you on as part time as it doesn't work at all with the job but once in you can change the job to suit your family.
Another thing to consider is the emotional effects. My DH has been though some harrowing times, and other we know have been through much worse on the job. It's really not easy and it can be more emotionally full on than most think. Over the years my DH has had to go to the gym to release anger (he's not normally an angry person), take the dogs for long walks to clear his head, been hospitalised etc etc
On the other side of it, my DH mostly loves his job any wouldnt change it or the world. If you feel you can take on the not so glam side of it, and cope well then go for it.
Sorry to be so negative but I feel its fairer to be honest. Maybe a PCSO role would be more suited as I believe the hours can be more flexible.