Having kids with vastly different needs is a tough balance. And since this is a first it would be a shame not to really share the full experience as a family.
I know it's expensive....but I think the BEST way to experience this in your situation would be to bring a family member who can babysit for a few hours at a time (is there a grandparent or cool aunt you trust in the picture?)? You could enjoy the park as a family for that time and discover things with your older kids (allowing them to go go go!), and then you (perhaps taking turns with the spouse) could go back to the room to check-in, feed, etc. ...And the whole group can be together for dinners, shopping, etc..
It just requires flexibility on your babysitter's part...and recognition that vacation experiences are gravy for them and they may not see much this trip. And you'll need to be ok with being pulled away from time to time to deal with baby's needs. Resort location may be key for this trip as well.