I thought I would relax over my coffee, I had to break up a fight between my two young sons about which television channel to watch.
Five ways to correct....
1. Separate the two clauses with a period.
I thought I would relax over my coffee. I had to break up a fight between my two young sons about which television channel to watch.
2. Separate the two clauses with a semi-colon.
I thought I would relax over my coffee; I had to break up a fight between my two young sons about which television channel to watch.
3. Connect the two clauses with a coordinating conjunction.
I thought I would relax over my coffee, for I had to break up a fight between my two young sons about which television channel to watch.
4. Change one of the independent clauses into a dependent clause using a subordinating conjunction.
Because I had to break up a fight between my two young sons about which television channel to watch, I thought I would relax over my coffee.
5. Use a conjunctive adverb to separate the two clauses.
I had to break up a fight between my two young sons about which television channel to watch; consequently, I thought I would relax over my coffee.