Ive installed over 5 upgraded sway bars on different vehicles and it has never made a car more stiff, only better on turns. CRV has some bad body roll...but as do other suv's in the the compact segment.Keep in mind that a higher performance sway bar would stiffen up the ride. Personally I find the CR-V is pretty controlled in this area and almost matches the class leading CX-5 while being more comfortable. Its a trade-off you might live with considering a new born would probably prefer smoothness over extreme cornering capability.
The civic and crv shares the same sway bars. Look up aftermarket sway bars from current gen civic. It should bolt right up.