There is actually no reason for gittle anymore. it provided some wrappers, most ofcwhich are now in dulwich.porcelain. Start with dulwich.porcelain. gittle also is not py3 compatible, though I have made some progress updating it for use in py3.
If you want the "simple button", just clone, push and pull into a single branch, dulwich.porcelain should be adequate.
The problem you will have with either of these is that dulwich does not have a merge capability. Which is needed when you start makng changes in two places and pushing to the same repo. Also, github sometimes refuses to accept s pull over https in dulwich,mthough ssh seems to work much better. I need to try to compare the ssh vs http push mechanism to see what is different ( the author doesn't use https, so it gets little attention)
gitview implemented really the very minimal set of functionality, yes the ui kind of sucks, but even that minimal set is not quite enough for it to be fully useful.. you need a clone button, a push button, a pull button, or at least a fetch and merge functionslity. you ought to hsve a way to select and checkout branches. you ought to have a way to select the remote. you need the ability to add or remove files to the index, and committing with a commit message (though i suppose you could simply default to adding all files and auto-committing). It helps to be able to diff files, and to have the ability to checkout previous versions of files.