I am also a children's book author (as yet unpublished in that dept!), I will try to help you with what I know:
With regards to illustration, unless you are as talented at art as you are writing, most publishers prefer you don't submit with illustrations. The tendency becomes to look foremost at the pics rather than the words, so no, don't illustrate unless you are brilliant!!
Where to go next, well, you can join a critique group, try going somewhere like Verla Kay's website or there are a few other children's book websites with forums where you can ask around. i haven't joined a critique as yet, partly because I am still fairly new to doing this more professionally and I haven't yet managed to get my day organised to suit writing, so couldn't give up to critique for others, which is the arrangement obviously.
In terms of getting them published you want to check out jacketflap. It gives the publisher websites, this is where you need to really research. Find publishers who work with the kinds of books yours is, check if they take inquiries or even unsolicited manuscripts, create a good cover letter and again, take information from some of the writing websites I have already mentioned. There is a ton of good advice out there - purple crayon is a nother good site.
Good luck and don't give up, I am on my second rejection so still a looooong way to go!!