Plan to fly to Rome from IAD then fly out of VCE to LHR for a one day layover and back to IAD - Family of 4 - 3 adults and 1 teen under 18. When I try to book this as a multi-city ticket, BA puts the price at over $9K. If I book a round trip to IAD-LHR and then individual tickets from LHR to ROM and VCE to LHR I can get the price significantly lower. We plan on taking 3 carry-ons and check one bag. Questions for the group:

1. On the first leg, when I land at LHR do I have to retrieve my one checked bag from the luggage pick-up or will it get transferred to the LHR-ROM flight automatically if I show the ticket when I first check in at IAD? (Remember - I have a separate ticket for LHR-ROM)
2. If the answer to the first question is Yes - I have to go pick up my checked bag - Do I have to go through Customs to pick up my bag and how long will that take?
3. I assume if I pick up my bag I have to go through security again at LHR How long should I give myself?
4. Does my entire family have to go pick up the bag or can they wait in the Terminal for the next flight while I go retrieve the bag and go through security again?
5. Finally - with a family of four traveling on BA should I pay to reserve the seat? - We don't want to be split up but not sure if BA assigns families together. Anyone have experience with this?

Thanks for the help - would be easier if BA site was better.