I have a hen sitting on a nest in the doghouse, of all places! It's quite a distance from the coop and the temps are in the 90s. Should I put water/food in the doghouse with her or is she likely leaving when I'm not paying attention?
She's leaving when you aren't paying attention.
When it is cold out, they may only leave for 15 minutes or so. When it is hot, they may leave for an hour or two. If you aren't out there all the time, you will miss the excursions.
It wouldn't hurt to put food and water by the dog house. It doesn't need to be IN the dog house because she'll come off the nest approximately once a day to defecate, eat, drink, stretch and dust bathe.
Is the doghouse in a predator proof area?
Unfortunately, it is on the ground and not predator proof. Should I try moving her? We do have 2 outside dogs who do a fairly good job keeping critters ran off...
Moving her, unless she is in last couple days of broody cycle, will likely cause her to break broodiness. Putting food out close to may increase attention given to nest site by predators. Water close should not be a problem.
Night time threats to hen and clutch can be reduced by obstructing entrance at dusk and removing it at dawn. This assumes dogs most effective during day.