Take the bus.
Buses between all parks except MK and EPCOT.
To simplify things i would just dine at the park you will be at for the day. It will eat up a lot of time to dine at CP and then take the bus to AK. Just a thought. Or if you really want to park hop then just do breakfast - spend time at MK until early afternoon then head to AK.
Trying to work out my dining options (not more than one TS/day) and pondering a CP breakfast then hop over to DAK.
I think you may have to take the boat or monorail over to the Transportation and Ticket Center and catch a bus from there. The only buses actually at the MK gates are to resorts, and all buses from MK to other parks are technically from the TTC. Or you can walk over to the Contemporary and catch a bus to DAK from there. For whatever reason, although you can get a direct bus from DAK to MK, you can't do the reverse, MK to DAK, without a stop at TTC.
I think you may have to take the boat or monorail over to the Transportation and Ticket Center and catch a bus from there. The only buses actually at the MK gates are to resorts, and all buses from MK to other parks are technically from the TTC. Or you can walk over to the Contemporary and catch a bus to DAK from there. For whatever reason, although you can get a direct bus from DAK to MK, you can't do the reverse, MK to DAK, without a stop at TTC.