I have reached the MK maingate in about 5-10 minutes flat at the most on numerous occassions; we even arrived at this same time last year during construction because all the traffic kept on moving steadily with no holdups.
However, once you park your van in the lot, you will have to allow extra time to park, ride the tram to the TTC (the main ticketing area), and either ride the ferry boat or monorail on over to the MK which will take up some more time.
It's hard to pinpoint exactly 'on the nose' how much time it will take before you actually enter the MK.
But, I would say since you are definitely trying to allot time for PS, I would say give yourself at the most a very generous amount of atleast 45 minutes to an hour head start from leaving your hotel so you will be sure and have more than enough time to reasonably make it without feeling like you have to rush in any way.
If you already have your tickets and don't need to stop at the ticket window and get them, this will also save you significant time. In the past when getting from point A (parking in the lot) to point B (walking inside the MK), it has taken no more than 20-25 maximum (sometimes we have even luckily beat that time).
Sometimes are definitely shorter than others because once you get to the main ticketing area, there may or may not be a monorail or ferry boat there already to take you over to the MK, but if not then you won't have no more than around a 5-12 min. max wait (also you might be approaching just as one pulls up) until one arrives.
Hope this helps.