Does sound like you are worried.

If your daughter is under 11 then you can OLCI (On Line Check In) 3 days before departure, so you should be OK for seats together. If not then it's down to an airport or on board juggle.

See the policy here.

I don't travel through LGW so often, but used to be fairly regular from TPA and MCO up until about a year ago. I have found in the recent past that LGW is loads better for bags than LHR. A direct flight ATL-LGW, I would guess you would be really unlucky to lose your bags. The major part of the LHR bag problems has been, but not exclusively, on transfer bags.

I'm sure a LGW BA regular long haul'er will offer their probably more up to date opinion on the bag situation.