First of all, your MIL should be reminded that people were fine for thousands of years without AC, and there is no connection between SIDS and AC. Of course you want everyone to be comfortable, but your MIL is creating a fear that doesn't need to be there. My neighbors across the street raised two kids without AC, and we live in an area that regularly has 15 100+ days a year every year. Those kids are perfectly healthy and fine.
Are you familiar with how each of these cooling options works? Some options are better than others, depending on the weather in your area.
A whole-house fan, for example, is only going to work well if your nights are reliably cooler than the days. The way it works is that you turn it on when the air temp outside is cooler than inside, and it exchanges the inside air for outside air. It can be extremely effective, but you might need extra vents installed, and it's not something that will help you if you want the house to be cooler than the outside temperature. Not sure of the cost, but it would be less than AC, but probably more than a window unit.
An attic fan moves the trapped hot air out of the attic but not out of the house. Cooling the attic air helps the house below stay a little cooler, but you're not going to notice a dramatic change if that's all you have. If you can have solar-powered attic fans installed, though, they will use almost no electricity, and they will complement other cooling efforts.
I'd suggest the following for starters: Keep the windows covered as much as possible during the hottest parts of the day. That doesn't mean it's going to be dark inside; usually just a crack of light is enough to light up the room without letting all the direct sunlight and heat in. Use fans as much as possible, and maybe splurge on window A/C units for the bedrooms if the bedrooms get hot and it's too hot to sleep well. You'd probably only need to run an AC unit in the evening. If that's not doing the trick, then maybe look into whole-house options.