I work two jobs in Ontario, Canada: a full time job during the weekdays (45 hours minus 2.5 hours for breaks) and a part time job on Saturdays.
My part-time employer is demanding that I work one more shift on Sundays (totaling 10 hours or more a week). I have told them that I am not willing to do an extra shift and they are not accommodating my request.
Can they legally force me to do this?
The thing is unless I've misunderstood the question neither of your employers is asking you to work 7 days a week - the "regular" job is asking you to work 5 days (which is pretty standard) and the part time one is asking you to work 2 days. So the question of "working 7 days" is something of a red herring here. I'm not trying to be insensitive - believe me working 7 days a week can be awful and I'm fully sympathetic to that, it's just not technically what either employer is asking you to do.
The real issue at hand is whether your part-time job can require you to work two days instead of one and to answer that will depend upon your employment contract with them (which should detail hours of work and any scope for changing them) and any local legislation surrounding change of working hours in an existing job.
As to whether they can "force" you to do the two days - well ultimately no but you may not be in a position to "force" them to continue giving you the existing one day either and that "no" may translate as "no, because you can resign".
EDIT:
A few more thoughts following updates from the OP:
There is a change coming in Ontario legislation that might apply:
In particular, employees can refuse shifts without detriment if they are asked to work with less than four days’ notice.
Unfortunately that isn't coming in to effect until January 2019 so that probably doesn't help you here.
If the day in dispute is a Sunday (which it sounds like it is) then that's a bit complicated but I believe that you will have the right to refuse to do so as long as you didn't agree to working Sundays when you were hired and that being the case they can't penalize you for refusing either.
Unless there is a contract in place, or some form of written agreement, they can schedule you for 2 shifts (or more).
Part time employment in Canada is considered anything less than 30 hours per week. So unless you have some form of prior agreement (preferably in writing) they are within their rights to schedule you as a part time employee (so up to 30 hours per week).
At this point, the best thing you can do is talk to the part time employer and tell them why you only want to work one day a week. At the end of the day, it is probably not worth it to the part time employer to keep you for one day a week if you are not willing to work more.
There is no legal issue here. You question is a tad misleading. You work a full time job AND also a part time job. No one is forcing you to work 7 days a week. You have one employer who wants you 5 days a week and one employer that wants you 2 days a week. As previously mentioned, they can schedule you up to 30 hours per week and that would still be considered part time. You can always say no to the shifts, but this will more than likely end with you losing the job to someone who will work 2 days (or more) per week.
There is a broader question here which also provides an answer for the OP: "can an employer force workers to work seven days (or more) in a row?"
Clearly if it is legal for a single employer to do this in Canada (Ontario), the OP will have no recourse in the case where the combination of two jobs results in this situation.
It's pretty common in the resource industries (maybe others) to work up to 14 days in a row, followed by a week or so off.
Longer than 14 days is not prohibited by labour law either as AFAIK, because it is sometimes done, but is often considered unsafe in situations where heavy equipment, etc. is involved -- so many companies discourage longer shifts for this reason.
