I just got another call back from a company I interviewed with last year (they actually have an opening now). When I sent them my initial information with my resume, I was completely up front about only wanting to work part time. They would prefer someone full time, but are interested in hiring me anyway despite my need for a 3 day work week (I have a two year old as well). At my old job, when I returned from maternity leave, they refused to let me work less than 4 full days a week, despite my long term good status with the company and the fact that they did not want to quit. Four days is much better than 5, but was still overwhelming for me with a new baby. I don't think they ever hired anyone just to work 4 days a week, but allowed several working parents that were already employees more flexible hours with a pay cut (not paying you for the hours you aren't there) after they had children. So, I guess what I'm saying is that it can happen both ways. A lot really depends on the companies needs. If they need someone to be able to be in the office all day, every single day, they aren't going to be as flexible.
You need to consider if you will take the job even if it's full time. I was not going to consider working 40+ hours a week, so it would be a waste of everyone's time for me to mislead a potential employer into thinking I was going to work full-time. However, I'm sure a lot of people tossed out my resume purely because of my desire to work part time. If you need and want the job, regardless of the full-time/part-time hours, I would not discuss it until the subject of working hours was breached in an interview. At that time, I would inquire about the typical hours, if people were typically in the workplace all day or working at home or on the road, if they offered flexible hours, etc. It's definitely a touchy subject for some, so you do have to be careful about how and when to approach the subject. Sorry, if that's not 100% clear. Hopefully, you'll get some more feedback.