L.N.
Hi E., sounds like you have a lot on your plate!
It also sounds like both of you are trying tactics that are not working/not acceptable. Soooooooo...
More information - what are you grounding your son for?
Obviously this tactic is not working. And your son running away is a message that he thinks your consequences are unreasonable. (I can't speak to whether they are or not since you didn't include enough info)
so he, in his young and youthful stage is escalating things but still the root problem is not getting addressed.
2nd - bad language. Where is he getting this from? Do you ever use it on him? Does anyone else? If you don't, maybe someone else is and he is trying to verbalize it to you (unpleasant as it is). Regardless, it is still unacceptable. I would, if you could, plan a special trip with him and you and your husband. Plan on it as a time to get away from the house and things that trigger these bouts.
Make it special, and figure out a way to talk to him about these issues when everyone is in a good mood. If he doesn't talk to you, figure out a mentor person older adult who he might and ask him/her to intervene for you and have the conversation.
Figure out solutions you both can live with and agree to. It does take being firm. You need to stand up for your values so that he will respect them. My guess is, on his part, he does not feel respected himself so he is running away. But if you continue to let him do this, you will teach hiim that running away from his problems is a viable solution.
One book i've been reading is "How to talk so your teen will listen, how to listen so your teen will talk". It's got a lot of real-life situations and solutions.