Allowing makeup work might be this teacher's attempt to save her own @$$. If too many of her students fail, her job is on the line. Heck, in some schools, if too many of her students score Cs and under, she could be in line for a pink slip. But the line about "it doesn't look like an English teacher's signature" was unnecessary (rather rude) and unclear. Rather "I'm concerned that because of the time stamp and illegible signature on this paper, Shane may have forged it. I've scanned and attached a copy of it. Please let me know if you've seen it before," would be the appropriate way to handle what I could consider potential cheating.
It sounds like both of you are frustrated, annoyed, and having trouble making yourselves understood. It's definitely time to sit down-- without Shane and with Shane-- and figure out what the heck is going on. If the teacher can't manage her classroom (Only some students got the extra/makeup work? Only some got specific homework assignments? That's not fair to any of them.) the principal needs to know. If Shane is forging your signature and only half-completing last chance assignments, you need to know. In my mind, the forgery is more of a concern than the failed homework. At least, if you're going to be lazy about assignments, have the courage to own that decision. Lying about it just makes it worse.