Since Access isn't a true mobile technology, a remote access solution like Wayk Now (or Remote Desktop, VNC, TeamViewer, etc, etc) would likely be your best option. However, as you say, the experience is likely to be clunky and you'd have to weigh the convenience against the benefits of using a more suitable technology (exposing the database as a true web application or native app would give the best experience).
There are difficulties driving the traditional PC interface using a mobile device touchscreen - the iPad now has some limited mouse and keyboard support, but not the iPhone. Desktop controls (like checkboxes) don't lend themselves well to a touch environment, because the targets that you need to touch end up being extremely small.
I'm not quite sure what you mean by auto-resize? In Wayk Now, you can use the typical "pinch" and "spread" gestures to zoom in-and-out of the remote display. When the display is zoomed, you can pan around by dragging the mouse pointer to the screen's edge. So you can feasibly zoom the display to make the checkboxes / touch targets large enough to interact with, but then you are very limited in what else can be seen on the screen until zooming back out.
So, while it's certainly possible to get things done with such a setup, it's certainly not ideal. I agree that "clunky at best" would be a fair description.
Coincidentally, we did have a feature request recently for some changes to the input mode on iOS that could make things work "slightly" better in your scenario.
Ultimately, if you are committed to the Access solution and need remote access via iPhone or other mobile device; then Wayk Now or a similar product is the kind of tool you should be looking at, but you will be forced to deal with some pretty large limitations.
Thanks and kind regards,