It is certainly possible to go to school with a tribe of kids at home, LOL!I am a 28 year old SAHM myself. When I did my Master's, my kids were 1, 1, 2, 6, and 7. Five in all.....the only thing about you situation is the newborn. Mine were small, but not that small. In my experience, the smaller they are the less predictability you can have in planning. My newborns had ridiculous sleep schedules, so I would have been hard pressed to schedule my study time around their sleeping, which is really the best way to go when you are a mom of very small ones like that.
The English and speech may be pretty doable, as there is no real studying for those, but writing instead. The Math and Medical Terminology would be bigger problems, as a lot of studying and memorization is involved. Mind you, I am challenged with Math and such under even the best circumstances. This may not be the case for you. If it were me, I would just take the English and Speech. If you are determined to take more, then you may want to CHOOSE one of the others.
I understand how it is when you want to get a jump on things. But, bear in mind with the fierce amount of competition for slots in Nursing programs, you want to get the best grades possible. Rather take a little less on at a time to achieve that than put yourself at risk for spreading yourself too thin with class and kids and get mediocre grades, thereby making it that much harder to get in somewhere. Hope this helps you, and good luck!