Seems to be par for the course for this family. They didn't like the answers (or lack thereof) that they were getting from LE/FBI at the beginning of the case, so they hired Mr. Vilt. They don't like Mr. Vilt's conclusions, so they fire him and hire another investigator to find the answers THEY want to hear. When they don't like Mr. Klein's conclusions, they not only fire him, but hire yet another party (an attorney) and threaten to SUE Klein. Do you see a pattern here? WASH. RINSE. REPEAT.
I would say it's a stretch to say they hired Allen Browning to "threaten to SUE Klein". They exercised their legal right to obtain legal counsel. IIRC Mr. Browning was DDK's attorney prior to all this, VDK retained Browning once he was named a suspect, and JM came on board once Klein started his media campaign.
In addition, I'm positive if both JM & VDK are charged Browning will advise one of the two to seek separate counsel.