After being jailed by Fredegund, how did Brunhilda get out of jail to be able to marry Merovech?

When it is said Brunhilde was "jailed", we shouldn't imagine she was put in a cell but as Gregorius of Tours said it was "sent in exile in Rouen" (V, 1). Even if the queen was far from having the same power and prestige she got in the 580's, she was still an high born princess, while her son Childeric was still hosted by his uncle Guntram, and it would have been unwise to burn all the bridges at once executing or treating her poorly for Chilperic.

It's not to say that she was free to maintain the royal court and administration she bagan to create in Metz during Sigibert's reign, but even if we don't know the details of her imprisonment, we'd be talking of a relatively convenable if imposed exile in a city that supported Chilperic so far, possibly before being forcefully sent into a nunnery once the matter of Childeric II and Guntramm being settled.

Interestingly, this fate was spared to her by her marriage with Merovech that she might well have accepted rather than insigated. Merovech himself might have been unsure about his succession : indeed, his own mother Audovera had been repudiated by Childepric in order being able to marry Galswintha and as Fredegund. The latter having given birth to a son of Chilperic named Samson, Merovech might have feared that his own succession would have been more limited or even wholly challenged giving Fredegund's ambitions (his own fate and what happened to his siblings didn't exactly prove him wrong).

Marrying his aunt-by-alliance was sketchy canonically but a good way to reinforce his own power, giving she was acknowledged as queen by Sigibert (which wasn't systematical for a royal concubine or a spouse) possily hoping to gain power and legitimacy in Austrasia against his father and his spouse, especially as Chilperic's deeds weren't exactly without their bad consequences.

Why was Brunhilda exiled by her grandson Theudebert II?

It's not really clear, but if we trust the sequence of events as set by the Pseudo-Fredegar, it was preceded by Wintrio's death "instigated by Brunhilde" in the "third year of Theudebert's reign". It's possible this murder or execution was felt by Austrasian nobility as irregular : indeed, while the regency by the queen mother was somewhat expected or at least considered legitimate, a regency by the grand-mother was outside normality.

This Austrasian nobility was a new one, not only because of the generational gap (increased by the apparent disappearance of several families during the civil wars) but also because this aristocracy adopted new values, more distant from the Merovingian public service "late Empire-style" and beginning to adopt more military, local, independent minded values.

A pressure from Austrasian nobility on a young king possibly anxious to access the entirety of his royal power could be expected there.

Any book recommendations are appreciated.

I'd very strongly suggest La reine Brunehaut (Bruno Dumézil, Fayard, 2008) for a more complete and recent biography made by a specialist of the period.