If this child was in child care they'd be down to one nap per day already. In child care when a child turns one year old they move to the toddler room, some facilities have 2 toddler rooms. One where they are still learning to walk and toddle and the other is for older toddlers from walking really well up to their 2nd birthday when they move to a pres-school room with lesson plans and a curriculum that is for educational purposes.
A 2.5 year old is really too old for a toddler bed but if that's all you have then it will have to do. Most toddler beds are done with baby bed mattresses. They're built for the weight of babies and not pre-school age kids.
So if they start acting like the bed isn't comfortable then it's likely they weigh too much and need to go to their regular bed that they'll have until college. We started them off on queen size.
Back to my point though.....this baby is well old enough to stop taking any naps except the same one your child is taking. Keep them awake until lunch them put them both down. I've never been a big fan of waking sleeping children but sometimes you have to.
So for the kids I'd do breakfast, stuff, snack around 9:15, stuff, lunch around 11 or 11:30 then down by noon so that baby could have a good 3 hours if they need it and they should both be up by the time you have to go do kid pick up and any errands.