Will this setup work?
Can I eliminate either switch?
And Use 1 router to pass the 2nd Public IP to 2nd router?
Will it work with 1 AP interfacing to 2 routers each with own hotspot?
Can this be done with one router?
Thanks
Budget constraints aren't fun. Still I think VLANs are the way to go. You can pick up a used Dell PowerConnect for $20 and use just one switch for everything, there are other options. Hell, the 250GS from Mikrotik might (should) work for this. As long as the APs can do VLANs and support multiple SSIDs you can do both networks on each AP.
But if you really need to balance things, do just one network per AP and keep an eye on things, and move the APs over to the other network as one network has too many users. Try to plan out the area and where people will be so you can minimize that. It's absolutely doable, though.
Given your constraints of course you cannot eliminate either router.