Some of this you may like, and some of it you may not. LOL
Generally speaking, a US citizen can come to Canada as a visitor for a period of six months. A person can apply for an extension to that 6-month visa while in Canada. To be granted the extension, there must be an acceptable reason given for the necessity of the extension.
I said "generally speaking" above because no non-citizen or resident is guaranteed entry to Canada. Usually, immigration officers like to have some assurance that a person who says they are coming to visit, means it. That assurance can be in the form of a return plane ticket, the presence of a permanent residence in the US, etc. If the immigration officer is not satisfied that a person intends to leave after 6 months, they may restrict the length of the visit or refuse entry outright.
The fact you have some distant relatives living in Canada likely won't influence the situation except in that your daughter could claim she was coming to visit family.
Your daughter could also choose to try and enter Canada by applying to a Canadian educational facility and getting a student visa, or she could try and acquire a job offer which would qualify her for a work purposes visa.
Both of those options are unlikely.
If your daughter enters Canada as a visitor, she will not be legally allowed to work, nor will she be covered by the government health plan.
Let's say she enters as a visitor, things go swimmingly with the boyfriend, and wedding bells chime across the tundra ( tundra is the frozen, treeless plain of the far north, not a Japanese truck). Assuming there is no US divorce to muddy the waters, your daughter can marry a Canadian with no special dispensation. Once she is married, she could then apply, from within Canada, to become a Permanent Resident with her husband as her sponsor. She would be allowed to stay in Canada while her application was being processed as long as her visitor visa was kept current.
Like all government processes, this one require a multitude of forms, physical exams, and fees. Count on it taking anywhere from 8 to 24 months for applications to processed and approved. Once approved as a Permanent Resident, she would eligible to apply for a Social Insurance Number and obtain employment.
I can certainly understand your frustration with your daughter quitting school when she is so close to her degree. If she has waited several years to be with this fellow, why the big rush now? But as you pointed out, sometimes the more you object, the more determined the other person gets.
Sadly, she's a big girl who may have to make her own mistakes. Life was probably a lot simpler when you could send her to her room without supper.
For more information, you can visit the Immigration Canada web site:
www.cic.gc.ca
Good luck.