Does my belly button or drain incision look infected? (photos)

The rash around the belly button and around the incision looks like Polysporin related to me.  If you are using this topical antibiotic you should stop it.  The wound separation is likely a stitch that is spitting.  Once it is removed by the plastic surgeon, it will heal rapidly.

You appear to have some degree of wound separation and skin irritation. Keep the areas clean and go see your plastic surgeon in person so you can be properly examined and evaluated and treated if necessary in a timely manner!

This looks like two separate things--a rash that has the shape of what may have been steristrips, and some minor wound separation. This does not look like any kind of emergency, so seeing to you kids appointments seems reasonable. Until you can see your surgeon, getting in the shower a couple times a day and keeping a clean dressing over the areas is appropriate. All the best.