Before my wife ends up stranded in T5 departures with all our bags, I thought I'd run past the wisdom of planned scenario on here.

Flying on BA metal in Y to NYC one early evening next week, wife and I on one booking (avios 241), young child on another (cash, HBO), linked PNRs.
Our plan is that my (Silver) wife arrives at Heathrow first thing in the morning in taxi, checks in 2 bags (ticketed allowance plus status allowance), and then does a day's work from the B-gates lounge.
I will be working from home, child at daycare, and we will arrive later in the day, check in child in F-Wing, meet wife in lounge and then board.

My questions as follows:
1. will she be allowed to check bags without rest of booked party being present?
We will both (try) to check in online the previous evening, but of course there are instances where this is not possible and document check is required at airport.
2. if I'm NOT fully checked in when she comes to drop bags, will that be a problem?
3. If she tries to drop off 3 bags (i.e. whole party namely 2 of hers, one of mine), will this be possible if I'm not present? In reality third bag would be small/roll case that I could manhandle with stroller if necessary but would rather not if it can go in a taxi!

4. Will we likely face any problems with only one party of the linked 'adult' booking being present when it comes to my checking in child later in the day?

The only reason we are doing this is that wife cannot finish work and get to the airport in time for the flight, and if we all go as a family work will be impossible with a young child to entertain all day at the airport. Now I've written it up, along with 4 potential pitfalls, and knowing BA/airport peculiarities, what seems superficially straightforward could provide plenty of opportunities for hiccups :-p

Thanks for any guidance that can be provided.