Minivan hater here... For someone that's not very tall, minivans are extremely uncomfortable to drive. Most don't think about that.
I'd say an Expedition would be the most vehicle (without being too big or too small), would fit the seats mentioned comfortably, and not overly pricey.
I know a ton of people love their crossovers too. I have a small crossover that is extremely comfortable to drive and it wasn't over the top expensive. I bought a used Saturn Vue, but I only have a booster and a convertible car seat in my back seat. Would it work with an infant seat too? Probably, but I'd say either a mid-size SUV or a larger crossover would be adequate.
Ford Expedition
Chevy Traverse (Saturn Outlook is the same) - Every Saturn owner I know has had luck with them... Only reason I went that route. I miss my Jeep Wrangler (but it's not practical with the family).
Dodge Durango (with 3rd row)
Dodge Nitro (with 3rd row)
Ford Flex
Jeep Commander (my ex's new wife loves hers - 3 kids fit well (my daughter 7, her older son 7, and her younger son 4))
Volvo XC90 (loved driving that on the high speed track while working at Ford) (yes, Volvo is 51% Ford owned)
It all depends on whether you want new, used, and your budget! If you need any info, I'm a mechanic by trade! I know a lot about the above mentioned!