Any attorney with sense would have counseled them that charges might occur and they should not leave town. There's no way to argue that they are acting responsibly or in innocent ignorance. Even if they didn't know they were going to be charged, it's highly likely that they've known for hours now that they have been charged and are wanted. A phone call, one phone call could clear things up.

The prosecutor doesn't need to time the charges for the convenience of the people being charged. There's no "fair trial" involved here. The trial will not occur for a long time, if ever. The details for any additional charges re fleeing will be worked out later as well. However anyone wants to slice it, they skipped town, deserted their child, and are now evading capture. Any negative public perception is all on them -- no one else but them.