First, welcome to Flyertalk ReginaMPA , hope you enjoy your stay here. I was happy to reply to your post as I'm in a similar situation, though my daughter is a year older than yours, with a similar aged son .

As it currently stands in the old system, my 3 year old has had no problems earning Tier Points, achieving status, earning vouchers - and importantly for you, contributing and allowing me to spend them from the household account I have. I believe the key points from BA are that a child can't exist outside of a household account (i.e. you can't create a 5yo a separate account), and if your 2 year old rang up BA and tried to individually take an action (!), they wouldn't be able to transact. However as far as I can tell when logging into her BA account online, there is no reason my 3yo couldn't book her own flights/use avios as the account looks the same as my adult one. The T&Cs also say that under 18 years old can't earn vouchers and they should be given to the household head, but that isn't the case and my daughter has her own vouchers assigned. So I don't entirely believe that BA's technology systems align with what is written down - of course that does create some risk that they align it with them, but I hope that isn't a big risk.

And my 1yo "infant" definitely doesn't earn points/status, and most airlines don't let him enter any frequent flyer details. But as soon as you pay for a seat, you do earn the points/status - so due to some complex routing my daughter's first seat had to be when she was about 18 months old, and she earned the status points/Avios then.

Turning to your point about splitting the tier points on holidays, I don't think your idea of removing the child's executive club number will work. From the BA FAQ, there are three parts in the answer, with my numbering (as at the time of this post) - Can I still earn Tier Points for British Airways Holidays package bookings?
i) Tier Points will be evenly split between the number of people on the booking.
ii) All passengers who have added a British Airways Club number will receive their Tier Points after the trip is complete.
iii) Infants under two can’t earn Tier Points on a British Airways Holidays package.

So that means to me:
1) They will divide the number of tier points by the number of people over two no matter what
2) If you don't enter a BA Club number, then the tier points will be "lost" for anyone without a number
3) Even if paying for a seat it looks like the infant can't earn points

I am slightly doubtful on #3, but think the number of 1yos who pay for a seat is pretty limited so they are just trying to simplify in the FAQ

Nobody really knows of course till the new system is fully implemented (as far as I know, I haven't followed the threads in great detail), and maybe there is a loophole around removing the executive club numbers, but that would be simple for BA to fix to align with the intent - as otherwise most of the people on this forum would be removing all other guest's details on holidays to try and boost spending for them as individuals.

Just to mention, one other "workaround" that has been suggested is booking the other family members flights separately from the holiday (i.e. you book your flight+hotel+car for you plus the infant, then your partner + daughter book a separate flight, noting that most airlines only allow one smaller child per one adult and you'd struggle to book a 2yo a separate ticket). This would probably work better in your case with kids than for adults, as most hotels wouldn't object around having a small kid in a room as they would having another adult. You would have a few more potential challenges about seating together and protection in case of IRROPs (i.e. when something goes wrong and the flight is cancelled or seriously delayed), but again, I've taken my kids around the world a few times on 2 tickets (one for each adult) due to challenges in getting 3 seats in first class on some airlines (looking at you QR!) without any concerns personally - but we are experienced travellers who go on planes a "fair" amount.