That's rough the whole family is seeing sluggish messaging thesford. I have a few thoughts on how to help with this.
First off, I would ask that you remove any 3rd party applications or keyboards that may have been downloaded to the phone and give it a restart. Sometimes downloads like this can cause messaging mishaps.
You could also clear the app cache as well using the steps here on the support form. Steps will be listed in the Apps link under the How tos section of the phone you select. You would also want to make sure the software for each phone is up to date. This information can be found on the home page of the device you search for here on the support site.
They last step I could recommend after that would be to Master Reset the phones using the steps you see in that link. (Depending on the exact type of Samsung phones each person is using, the steps may be slightly different)