Gosh I am sorry I didn't see this earlier! Right lets see....
You are correct in thinking there is a bus that goes to the "park", it's the "E-line". Though to be honest, they stop running in the evening really early so in this case you will either need to a taxi. As stated, they are roughly around £6.00. I'm going to have a look for the bus time table online and link it in when I've posted this.
The station side you want is Ashford International Eurostar Terminal. It's is in fact the same station, but domestic trains have an entrance on one side, and the Eurostar on the other. You can access domestic trains via Eurostar but not vice versa. Can I ask why you have to do a total of eight trips? Is the first lot back and forth, back and forth because of the number of people in your party? Depending on what time you arrive before DLP, the bus may be an advantage, but they all leave from the domestic side, which would mean you walking right around the station.......there is a dayrider ticket you can buy for £3.20 adult and £1.15 per child which will enable you to travel on all stagecoach buses all day. You can swap these around with adults and children to use at different times though
You can PM me if you need any other help, it's times like this when I wished I could actually drive LOL!

Right, off to find the link
~Edit~
http://www.stagecoachbus.com/PdfUploads/Timetable_6582_%20E%20LINE%20(Ashford).pdf