Pricing sounds reasonable, though I wouldn’t discount the kid’s menu as much, since kids can eat as much as adults when it comes to hotdogs and pizza. All you can eat always scares me from a profit standpoint and branding standpoint. It can cheapen your brand. I also prefer to get paid 100% before a catering event.
I find clients want to know exactly what an event is going to cost them up front and your option #2 doesn’t accomplish this. The nice thing with a hot dog cart catering is guests can’t load up their plates with multiple hotdogs at a time and cause the food to run out before everyone has a chance to eat. Pigs have to come back for 4ths and 5ths, etc.