That device is now too old to run the current version of the YouTube app. To bring that device up to a version of Android that has any kind of new app support will push it past any version that's going to run well on that device.
Bottom line - that device is very old as far as tech is concerned (released 9 years ago), it's time to look for a newer model. There are quite a few budget range tablets that will perform just as well on a newer version of Android.
If you need additional help or have more questions or details to share, please join the site so you can reply in this thread. See
this link for instructions on how to join Android Central.