YANBU to think this. But would you would be unwise to change your life because of it unless you really think you have no other option.
Some people are better off working fewer hours because of tax credits. However, tax credits are being reduced every year. You might be better off initially, but in a few years time you could find yourself substantially worse off. It is always better to avoid being at the mercy of successive government's whims.
Also, have you considered the longer term impact? Part-timers are more likely to be passed over for promotion and pay rises, meaning that ultimately you can pay a much higher price than just the immediate reduction in salary (which, as you say, may be topped up by TCs). And ultimately your DC will be grown up and you won't get any TCs at all (if they even exist by then anyway).
I am currently paying so much in childcare that I am left with less to spend on food and bills than someone on benefits. I consider it worth it though. In a few years time, when my childcare costs have reduced, I will feel an awful lot better off, have no off-putting gaps in my CV, managed to hang on to my house, and above all, kept the self-respect and sanity that can often be stripped from people on benefits who are constantly told they are 'scroungers' etc.
Ultimately, this is a long-term game. Financial pain now may be worth it in the long run because it really isn't a good idea to make yourself so vulnerable and dependent on state help unless you have no other choice. However, if things are really that bad that you're miserable and on the brink of financial collapse, then it may be your better option. But you should only consider it as a short-term plan to get yourselves back on a better footing.
DEfinitely go see the CAB or an independent debt advisory service. You'd be amazed at the amount of help you can get for debt management these days. I'd be very surprised if you couldn't get something worked out to make those debts more manageable.
Good luck. I can see why you feel like your running faster only to go backwards and I hope things improve for you.