Lets talk about money.

Does the new job offer pay better ?

If so, and it seems like a better job then definately got for it.

If the new offer pays less maybe think twice about taking up their offer.

If it's a LOT better and you get an offer, probably yes.

You are asking complete strangers from all walks of life what to do with your life decisions? Do you not have a support system of friends or family? Sad. Learn to decide what's best for you.

If you can swing it without pissing off your current job and you think it might end up being a better job then go ahead and take it and see what you think. No reason not to give the new job a shot but it easily may not work out so I'd stick with the first job until you know.

You need to learn to make your own decisions.

It's just business. You need to do what you need to in order to take care of yourself and family.

That being said, here is something to keep in mind. Leaving one job after a short amount of time can be explained. "The job was not the right fit for me." Leaving multiple jobs in short order in a row looks bad for you. What that means is, if you do take the new job and it turns out to suck worse than this one, you may find yourself stuck for a while. So, just be REALLY sure that you want the new one before taking it.

Take the better offer so long as it is truly better.

If the new place only want you to do ONE trial shift, then I would be tempted to ask for holiday from your current place that day or phone in sick - so you can do the shift and then take it from there

If you have been asked to do a trial shift - then you haven't got another job (as yet) to go to