I'm coming a bit late to this but would like to make a couple of points.
Firstly, it has not been decreed that flexible working is a right for parents. Businesses must consider a request, but as long as they follow the correct procedure, there are fairly broad business reasons they can give to refuse if they want to.
Secondly, I really can't see any logic for wanting to be paid pro rata more because you are part time. You can't have it both ways. If you are lucky enough to have an employer that can accommodate part time working for you then asking for a pay rise as well is pushing it a bit.
In terms of being more productive, it's all about the individual. Some full timers are very productive, working many hours over and above their contract and/or being more productive than others during the normal day. Some clock watch, don't get much done and are off at 5.01pm. Similarly with part timers, there are some of both.
In my personal experience, coming from environments where 9-5 was a notional concept on a contract rather than actual working hours, for senior staff anyway, part timers have usually worked less hours pro rata for equivalent pay, purely because most part timers I have encountered have been (usually) women who are reducing their hours to fit in with nursery times/school pick-up, and other things that require them to leave by a certain time. In other words, people who used to work more than contracted hours when full time often work only contracted hours when part time, because there is a reason to leave on time. I'm not saying that's bad, probably the long hours worked previously and by others are bad, but that's often been the scenario I've seen.
Obviously that's not always the case anyway, and often part timers do more than their fair share to make sure they can keep and justify those hours. Equally obviously long hours doesn't necessarily equal more or better quality output.
I suppose my point is you can't make generalisations about how productive people are just because of the hours they happen to work. Most people are paid a set salary for doing a set contracted number of hours, so unless you are paid in some kind of productivity-based way, within that salary structure there are always going to be some who earn it more than others.
Hopefully, hard-working productive staff get rewarded in terms of increases and bonuses where applicable (not much at the moment obviously!), or at least in terms of personal recognition, trust, and career development. That's what you'd hope anyway.
The bottom line is when you are a parent, if you want to work, there are usually childcare costs, so your income is going to take a dive either way. If you choose to work part time and save on childcare costs, your income is going to dive as well. But isn't it marvellous that there is a mechanism in place now for parents to request different working arrangements to fit around their children, and isn't it brilliant that doing so is becoming more and more normal? I think so.