If you go for care work, there are often hours to suit, and they are used to mothers of young children. (I am a care worker and toddlermummy).
For part-time work, you will probably be offered 6am to 10 am, or 4pm til10 pm,. The full time shift pattern is often 7;30 am to 2;30 pm, 2pm to 8;30 or 9;30 pm, and a night shift is 8 or 9;30 pm til when ever the morning shift starts. If you are only nineteen, try to go somewhere that will pay you the FULL minimum wage ie; 4;85ph. You probebly won't be offered much more than that unless you live in a big city.
Try not to go anywhere that offers you the minimum wage for your age, because you will be expected to do the same amount of work, staff turnover can be very high and you could find yourself in supervision of someone who is paid more than you.
They are required by law to do a criminal record check, they are also required by law to offer you NVQ training. Don't let them charge you for this, they get it paid for by the government if you are under 25 (like me!)
It is a nice job if you can do it, it IS mostly commen sense, and as you have had a child I imagine your stomach isn't delicate and you can run a washing machine!!
Good luck, MS, I hope you find what you are looking for