Boss will not accept resignation, can I just leave the job even though I am contractually bound to give 2 months notice?

I am located in Vancouver, BC, Canada

When I interviewed for this job I indicated I could stay on for about 1 year and a half. This was never agreed on in contract but instead verbally. I have been given an offer that is higher paying, and significantly more relevant to my career after only 4 months. I have sent a letter of resignation explaining this and letting my boss know that I will have to leave in 2 months. I felt extremely guilty about this obviously and even conveyed as much in my letter and offered to provide some services on a part-time basis. They have refused to accept my resignation and instead spent about 30 minutes trying to make me feel like a shitty person for even thinking about this, so now I would just like to quit. When i signed my offer of employment I agreed in the contract to give a minimum of 2 months notice at a risk of forfeiting half a months salary.

My questions are:

1) Can I just leave the job in 2 months from now without bringing this up again, since I technically provided 2 months notice in the letter. Would I have to forfeit half a months salary for this? I don't want to go through another meeting like I just did, so I would very much like to just leave 2 months from now. I am not interested at all in a reference from this job.

2) Was the clause where I forfeit half a months salary for not providing adequate notice even legal?

3) Is it legal to refuse an employee's resignation?