It can be done if this is your passion and you are ready and willing to put in the time. I spoke to a woman who had 2 or 3 kids (can't remember) under the age of 5 and successfully completed an accelerated masters CNL program. You have to look at nursing school like it is a full-time job which means putting your children in daycare from 8-5 Monday through Friday and when your not in class you spend the rest of the time in the library studying. If you scour the boards on here lots of people talk about it and have great success stories. The biggest advice I would give to you is TIME MANAGEMENT. I think you could definitely succeed in a nursing program
given your circumstances if you diligently apply yourself.
I agree with all the post above about researching and spending time writing an essay that tells your story. The essay is the one chance you get to market yourself so write, rewrite and revise until its perfect. Also, be sure to answer the questions asked in the application. The last thing an admissions counselor wants to read is a 3 page essay that skated by the questions. Don't use the same essay for each school. I would think it would appear obvious if you wrote one essay and then mailed it to three different schools. Research the schools, find out what they are known for, the type of research done in the school, basically get to know the school so you can touch on how that caters to your long-term professional goals in your essays and stick to the word count. My mother is the assistant dean of a school and she always told me even with college essays if the professor and/or application states 500-750 words then don't type 400 or 800. Stick to the count. it shows you can follow directions.
I had the GRE waived for the school I applied too so I don't have a lot of feedback in that department. A lot of schools weigh heavily on the essays and recommendations. Make sure whoever writes it for you actually knows your potential and can speak to your strong suits. I was so thankful to have such great people to write mine.
I urge you to move forward with this passion, explore it, and I think you will be fine. Obviously, based off your previous background with two bachelors and a masters that you are well equipped to handle the challenges.
As others noted, you can get your associates in nursing, however based on research a lot of hospitals are looking for graduates with a bsn or msn. I recommend before deciding that route that you research the hospitals you may want to work and the hiring rate for adn's. The last thing I am sure you want is to graduate with an adn and not be hired anywhere quickly!
Best of luck to you!