There really isn't any reason why you can't use an exterior deck stain indoors. The only concern I can think of is the smell of the stain, but you would have strong smells with other finishing systems.

I suggest you buy some redwood, like your flooring, and do some samples of different deck stains. This way you can see the color before staining the floor and also see if this is the effect you are after.

Most exterior products are meant to be used outdoors therefore they have pesticides, mildewcides and other things that we are not supposed to to breathing in while we are indoors.

I used decking stain on my internal wooden floors 4 years ago and its still going strong with some wear evident now on high foot flow areas like the kitchen. But I say full-marks for using decking stain indeed! By the way I used Ronseal decking stain.

I can Not Believe You would encourage someone to use exterior product inside. That is why they are called exterior they are meant top be used "outside". Pesticide Mildewcides can cause cancers do you want your family breathing in these chemicals on a daily basis