Why is it a sham? 117 Tories was almost exclusively a Brexit protest and nothing more.
This is ONE issue, albeit an important one. Far from the only issue a government deals with though on a day to day basis right? (Although it doesn’t seem like it sometimes)
Plenty of Old Labour MPs in New Labour didn’t like Tony Blair and some of his policies but held rank along party lines generally because they liked having a centre left/Social Democratic government rather than a Tory one.
So why wouldn’t the Tories vote along party lines if their position in power is threatened?
What you are proposing, like Corbyn, is even more chaos at a time when the country does not need it.
May needs to head across the floor and deal with the right wing of the Labour Party and like minded moderates to come up with a solution that will win a majority in Parliament. That’s the way out of it. Time is not on her side though.