iphoto will not maintain my photo resolution when I crop it

I start off with a photo of 4352 x 2448

Okay, that's an image 4352 pixels by 2448 pixels.

I crop it to send for printing...

Cropping removes pixels. It literally cuts bits off the photograph. Why do you expect to have the same number of pixels after you've removed some?

DPI is more complex than that, btw. It entirely depends on the size you're printing at. You can have the same DPI with images that are both 4352 x 2448 and 1352 x 1743, just in the latter case the print will be smaller.

DPI means nothing in the digital world of your computer. There are no "inches" to have "dots per..." Size is measured in pixels. That's the same on your camera. It doesn't take 10 x 8 or 6 x 4 shots. It takes shots measured in megapixels. For instance 4,000 x 3,000 is a 12 megapixel camera.

Using that example, that shot from that camera has 12 million pixels. So that's how many "Dots" there are. To decide the ratio of dots per inch, you now need to decide the "inches" part. And that's printing. Print at 10 x 8 and the dpi will be 4,000/10 or about 400 dpi. At 6 x 4 then it's 4,000/6 or 660 dpi. Work the other way: Print at 300 dpi and the resulting image will be about 13 inches on the longer side.

So, your photo as a fixed number of pixels. Changing the dimensions of the print will vary the dpi, changing the dpi will vary the dimensions of the print.

For more see http://www.rideau-info.com/photos/mythdpi.html

It is not possible to keep the full pixel size of 4352 x 2448 pixels, when you crop a photo. The cropping removes pixels from the photo and changes the pixel size to the dimensions of the cropping rectangle. You can still print the cropped photo with the same dpi, just print it on a smaller paper size than the original, uncapped version.

The pixel size (width x height in pixel) is not the same as the resolution in dpi. The dpi (dots per inch) depend on the size of the printed photo in inches. To preserve the same dpi after cropping print the cropped photo on a smaller paper. 250 pixel per inch will give a good print quality, so you can print a cropped image of 1352 x 1743 pixels at a size of 5.4 inches times 7 inches.

There are tools like the Online Image Enlarger that can interpolate pixels to increase the pixel size while preserving the sharpness, but they will also enlarge artefacts. Online Image Enlarger

Try it, to double the pixel size of the cropped photo, if you want ta large print, but check the enlarged image carefully for artefacts, before you send it for printing.

There are also some apps that do a very good job of enlarging images. One such is Gigapixel AI from Topaz labs. Not free. Not cheap. But they offer a free trial if you want to give it a go.