semi modals - Is there an insinuation after 'had better'?

You’d better bloody well tell them you’ll need to discuss it with me first.
(The Casual Vacancy, by J. K. Rowling)

Whenever I saw a bare-infinitive follow close behind ‘had better,’ I thought ‘had better’-plus-verb is a loaf of meaning bread. But as you see, there’s a ‘bloody well’ intervention. This gives me this impression that the construction might be a combination of a matrix and a conditional clause - I mean two meaning-sub-breads. That is, ‘You had (in here, there might be an insinuation of ‘a treat, a situation, etc.’) better bloody well, (if you would) tell them you’ll need to discuss it with me first. As a to-infinitve can deliver a conditional meaning as in: People might take you for a girl, to hear you sing.
It’s hard to believe there could be any account for this in any grammar books. But do you perchance read the way I said?

Answer

It's an ingenious idea, and it has some historical support. When the idiom first arose (see OED 1,4,b), what is now the subject was a dative and the sense was It would be better for you, and you could certainly understand that as:

It would be better for you if you bloody well told them ...

But I don't think it works. I think you have to understand what follows better not as an adjunct but as a complement acting as an NP. Historically, in fact, it was the subject, expressed as a content clause with that:

Him wære betere Þæt he næfre ȝeboren nære ... = Him were better that he never born wasn’t = That he had never been born would be better for him.

Although the front end of the expression has changed drastically, I think that complement sense of the back end survives:

Tell them you’ll need to discuss it with me first is what you'd better bloody well do.

Let me offer you an alternate far-fetched analysis: ’d·better has become an ordinary modal verb, taking a bare infinitive (with its arguments) as its complement:

You’d better bloody well tell them ...
You should  bloody well tell them ...

This analysis may be a little more plausible in US speech, where the ’d at the beginning has practically disappeared:

You better f*****g tell them ..