Yes, some discomfort at the moment where the widest part of the toy is just about to pass through your sphincter IS normal, but at that point you need to pause and focus on relaxing your sphincter before you push it in any further. I know it's tempting to just shove it in, but breathe and give your muscles some time to adjust, and they will willingly open up and swallow the rest of the plug once they stop panicking about the fact that you're shoving something in there. Let your ass control the pace and practice patience and everything will go smoother in the long run...
Disposable enema kits are good, but be sure to replace the fluid inside the kit with clean, body-temperature water since those kits are meant to treat constipation and will irritate your rectum.