If I refuse a run, but later accept it, can the company force me into a voluntary quit because they don't want to fire me?
No company can force you to quit voluntarily. You either quit on your own, or you don’t. They can certainly fire you, if the offense is serious enough, but Canadian federal labor law demands the causes for dismissal to be clearly documented. If they told you from the outset that refusing a dispatch is a fireable offense, then they have a case. If the company has just decided that firing you would be convenient for them, or to prove a point to the other drivers, you may have a case against them. But it’s a case that may not be worth the trouble of pursuing.
When you suggest that the company is forcing you to quit, I assume you mean that they aren’t giving you very many miles or they are giving you all the lousy loads. If that’s the case, you might as well quit because the situation isn’t likely to improve. You might want to take the problem to a higher level within the company, over the dispatcher to the fleet supervisor, and see what can be done to resole the problem. But like I said, it’s not likely to improve.
Whether you pursue the problem is dependent on how much you have to gain in proving your point. If you’ve been around for a long time, and have accumulated lots of vacation time, or maybe seniority, then you should stay and fight. If it’s only a matter of a year or two, head for the door.
Also, if you had a justifiable reason for refusing the load, ie: out of hours or you had arranged for time off in advance, then you do have a case. But it all depends on what you have to gain by staying and fighting.
The best arrangement might be to voluntarily quit, after reminding the company that you do have some protection under federal labor law against unjustifiable dismissal, and asking them for a favorable written reference for subsequent employers. That way, they can’t stab you in the back while you’re looking for another job. And remember, driving jobs aren’t had to find these days.