You should be able to book FPs for all your onsite days, but you will have two separate 60 day windows. This assumes both resorts are Disney resorts, not sure about Swan, Dolphin or SoG or indeed the "good neighbour" hotels.
If you've booked FPs for other days, either before your first onsite stay, or for the days in between your resort stays, then I'm not sure what the impact will be.
I'm paging @Rob562 for help here, our resident expert on ticketing and FPs!
Yes you are capped we are AHP Platinum Plus we are staying at Beach Club for 7 days booked our FP’s then tried to book FP’s a two weeks ago on a Saturday to just go for the day and we were unable to, so I had to drop our FP’s for the last day for our week stay just to book the FP’s.
This part stinks for us being local and staying on property booking FP’s for our stay and trying to go on the weekend (we normally go to WDW 2-3 times a month).
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