Fiona,
I volunteer at my son's school and it never seems to affect my client work at all. I wrote a blog about volunteering
here.
At the end of the school year, a volunteer breakfast was held along with business partners who contribute money toward student programs. Most schools have this because of so many cuts to school budgets that it has become impossible to pay for music, arts and after school program without businesses purchasing the instruments, uniforms and snacks.
Anyway, when I least expected it...I met many business owners at the breakfast and exchanged business cards. In fact, even on the evenings when I volunteered at the school book fair, I handed out cards to parents who were business owners (if they asked).
My point being...you can still network even with small children and a full-time job. Consider every event you attend with them to be an opportunity to let people know what you do. Now, I'm not saying to make that the point of conversation because people don't like the 'salesy stuff' but when it comes up in conversation (and it will!), be ready with your elevator speech and business card. In fact hand out a few.
When school starts, there is typically an open-house. Ask if you can leave your flyers at the door. Offer to volunteer; even if you can work from home to help out a church or a school. It's a great way to network with people.
I know you have a FT job but many of these events are held in the evenings and weekends to accommodate working parents. Churches or synagogues need help on the weekends and often have child care available.