So you are stuck with SVN, huh? So here is what you will do:
git svn clone -s --prefix=origin/ https://svn.url/projects/{my_project}
This assumes that you have {my_project}/trunk
, {my_project}/tags
and {my_project}/branches
Work the same way as you work with git, except that:
Instead of pushing you:
git svn dcommit
And instead of pulling you:
git svn rebase
You can fetch by running the command:
git svn fetch
Avoid pushing/pulling to/form different sources. Use it as it was not a distributed versioning system.
Here is an example of script for testing how you can use git-svn.