My employer is trying to make me work some of my shifts in a different location (despite my contract stating the address of my work, with a vague clause as follows: "the Company may re-assign, reallocate or re-organize
your duties and responsibilities as circumstances change provided such changes do not constitute a
fundamental breach of contract or constructive dismissal as recognized by common law and the ESA"). The location is not extremely far away, however, it would add costs of transport that I currently do not have. Because of the nature of my work, I also start my shifts early in the morning, which would require me to have an even earlier start to my day in order to be on time - something that I did not sign up for when I took the job offer. It also adds additional stress as I would be dividing my work between different locations and environments.
Is there any way in which I could dispute this?

I am sorry to hear about the changes to your employment. These types of reassignment can be very stressful, especially when it feels like the employer is making your life harder for no reason or ignoring legitimate concerns.

You could try to dispute this, however, doing so would likely be very risky as you may have to treat this as a constructive dismissal and resign, then bring a legal action. The chance of success would be mixed, which is a problem as if you are unsuccessful, you are deemed to have resigned and entitled to nothing, including EI.

For a constructive dismissal, there needs to be a fundamental breach, not just any breach. This is context specific, and will depend on a lot of factors, such as if you drive. Given the contractual terms that may allow them to do this, the fact the new location is not extremely far away, and that there is not a reduction in pay, successfully arguing this may be difficult.