L.I.
I don't think you are pushing her to hard at all. As long as you make her learning activities fun and you go at her pace then I think that what you are doing is fine. If she does not want to do homework try to come up with alternative fun ways to teach her the same lesson as the homework. Maybe hit a few of those homeschooling websites for ideas.
I think it is ok to make her finish the last two classes expecially if you paid for them. Teaching kids responsibility and to finish what they start should begin at a young age. Going forward I would recommend letting her choose her own activities to get involved in and expalin to her up front that if she chooses it she must finish it.
My MIL does the same thing. Interject her opnion and two cents when no one is asking her. I remind her that it has been 39 years since she had a 3 year old and quite a few things have changed. I guess it is my tone when I remind her thst lets her know to shut up and butt out.