Sorry, but to the best of my knowledge there are no working credits payable in Spain.
Here is a link to a webpage which shows what benefits you may be entitled to and those you will not.
Hope that helps.
As for working in Spain, at the moment it is very difficult for most people to find work unless they are highly trained in specialist fields.
However, the good news is that one of the few types of jobs left in Spain right now is teaching English and you are considering that. So, if you are thinking of moving to a major city, then teaching English may well be a good idea.
The bad news is that you will probably have to work long, often unsocial hours, and work at several different places to make up your earnings, especially if you do not have a TEFL qualification or similar.
You will also probably have much more luck in this area (or any work area) if you can speak Spanish.
The other thing about teaching English is that, although you may be lucky enough to be taken on by a school or college, you would most likely find yourself working for a number of different private clients, many of whom will prefer to pay you cash in hand, no tax questions asked.
Which brings me to tax and insurance.
As you will be making a permanent move to Spain and working there, you will be expected to pay into the national system (and it is necessary in order for you and your children to be eligible for state healthcare).
Unless you can find one full time employer who will pay your taxes for you (after deducting them from your salary of course), you will have to go self employed, or autonomo.
Being autonomo means you will have to invoice your employers, file tax returns and pay around 260 euros each month in order to be registered for state health care. I believe there may be a lower payment for those doing low paid work in some areas, but either way, it would be advisable for you to employ a gestor experienced in tax payments to help you with this (not as bad as it sounds, gestors usually work for a reasonable sum).
However, having said all that, if you cannot find work, there may be another way to access the state services, but that would mean waiting for your parents to retire here. If either of them are receiving a UK state pension, once registered, they should be entitled to state health care for them and immediate family members.
That may be a bit of a safety net anyway.