I asked for help on this topic before our trip, and thought I would share how it all went for us (a family of 5 including 3 kids aged 8, 11 & 11). We wanted to go directly from the Cambodian border (Poipet) to Ayutthaya to connect with the sleeper train to Nong Khai (Laos border). We were going to Bangkok at the end of our trip, and also wanted the chance to see somewhere else in Thailand.
We bought our train tickets through asia-discovery.com Their service was great. We communicated with one person, the tickets were posted to NZ (and arrived 4 days after leaving Bangkok). You can pick them up at Bangkok train station if you want instead).
We took a private van to the Cambodia border. Once across there is a mini van/taxi stand on the left directly across from the shops. We arranged a taxi direct to Ayutthaya for 2700 baht. This was much more expensive than public transport of course (we didn't find out about buses as were under the pressure of time), but suited us and our time frame. We had a quick trip to Ayutthaya - about 4 hours from memory.
We didn't have time to stay in Ayutthaya, but had a few hours to look around. We took a tuk tuk tour of the main temples just for a look, and ate at the night market. We booked a room in the Baan Are Gong. This basic guesthouse is less than 5 minutes from the train station. We left our bags here while we looked around, and also had a shower before catching the train. It cost NZ$16 for the most basic room. The guy was so friendly that we felt quite bad about staying for only a few hours. We would love to go back here to stay properly. You can't book direct, but can through Agoda
We found that going through Ayutthaya and catching the train at 9.41pm was an efficient and enjoyable way to get between Cambodia and Laos if you don't want to fly.