COCKPIT DISTRACTIONS DURING CLRNC RECEIPT AND POORLY CONDUCTED BRIEFING OF FLT CREW RESULTS IN LOST COM AND ALT DEV OUT OF BWI.

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THE EVENT WAS AN ALTDEV ON DEP FROM RWY 28 AT BWI. WE THOUGHT WE HAD BEEN CLRED ON RWY HDG TO 10000 FT; BUT THE ACTUAL CLRNC WAS RWY HDG TO 4000 FT. THE PROB STARTED WITH AN ATC CLRNC THAT WAS COPIED INCORRECTLY. BOTH THE DEP FREQ AND ASSIGNED ALT WERE IN ERROR. THESE MISTAKES WERE NOT CAUGHT BY CLRNC CTL DURING THE READBACK. THERE WERE 2 YOUNG PAX IN THE COCKPIT WHICH CAUSED SOME CONFUSION AND NOISE DURING RECEIPT OF THE ATC CLRNC. THE BEFORE TKOF BRIEF INCLUDED THESE 2 ERRORS. WE DEPARTED RWY 28 ON HDG AND STARTED OUR CLB TO 10000 FT. PASSING THROUGH ABOUT 1500 FT; WE WERE TOLD TO CONTACT POTOMAC DEP. I SWITCHED TO THE WRONG FREQ AS WE CONTINUED OUR CLB. SINCE NO CONTACT WAS MADE WITH DEP; I SWITCHED BACK TO THE TWR FREQ AND WAS TOLD TO LEVEL OFF AT 7000 FT AND CONTACT POTOMAC ON 124.55. POTOMAC ASKED WHAT ALT WE HAD BEEN ASSIGNED AND I SAID 10000 FT. HE SAID THAT WAS WRONG AND THE ASSIGNED ALT IS ALWAYS 4000 FT. WE DISCUSSED BRIEFLY WHAT OCCURRED AND HE HANDED US OFF TO THE NEXT CTLR. 1) SLOW DOWN. DON'T HURRY DUE TO A LATE DEP. 2) NO KIDS IN THE COCKPIT DURING FLOWS IN COM WITH ATC. 3) ALWAYS ASK QUESTIONS WHEN IN DOUBT. I FELT THAT 10000 FT WAS TOO HIGH FOR THE DEP BUT DID NOT QUESTION THE FO'S CLRNC BRIEF.