Lots of positives here - known history, low miles, good maintenance, well sized for 5 people, good price.
Your brothers must be "in-to Mazdas" for some reason , right ? Don't kid yourself that regular maintenance , or major repairs would be any cheaper with a Toyota.
What does Toyota offer in this category , the Sienna minivan ? Uglier, doesn't drive as "sporty" as the mazda, nor handle or brake as well. MAybe a Toyota Venza - station wagon looking thing, certainly better looking than a sienna , there seem to be a lot of those owned by 60+ yr olds around here, I'm sure there are some low milage examples available, unsure on the pricing , but doubtfull you'll get one with 78K miles for $4K.
On the kids and the car seats, put the two car seats in the left and right sides of the middle row - let the oldest child climb over the middle seat into the back, to get into his/ her booster seat. I'm pretty sure the oldest will love the climb and having "her own row". Besides , I can't think of any cars with 6 doors, so unless you plan on putting the kids 3 across , it's climb over the middle seat or enter thru the back liftgate and climb over from there, no matter what vehicle you get....you want more kids, and to bring them and another adult with you , there are gonna be some tradeoffs. If you want to drive 7 with lots of elbow room you need a suburban , or escalade, expedition, etc....probably not worth it for low % of time grandparents will be sharing a ride.