If you pay to park at one park, then you are good to go for all parks for that day. If you valet park at a hotel, then you are good to go to valet at other hotels for the day. This does not transfer from hotels to parks - at least I’ve never heard of this being a thing. (I’m assuming you aren’t staying on property, because regular parking at the parks is free if you are. If you want preferred parking, you must pay an upgrade if you are on property.)