Things to do:
Vaccinations are going to be reviewed and administered by the panel physician after your case heads to the embassy. It's not something you need to get a jump on, the PP will review them at the appointment and fill out your DS-3025 which becomes your immunization record in the US for life. Might as well let him handle it.
Not sure about the K2 process with your children, I'll let others address that.
You probably have at least nine months (or longer) before the move. Our petition was submitted last August and my fiance will be here in two weeks. Granted there was a massive speedup on turnaround time at the end of 2023, they seem to be doing a lot of backlog cleanup at USCIS right now which may affect the speed by which cases are approved and forwarded to NVC. Even still, the time at NVC is a complete tossup as well, with cases taking everywhere from a few weeks to years to move to the embassy. Ours was projected to sit at NVC 3-4 weeks; it did not move for nearly five months.
Patience, above else, is key. I know what it's like to be excited about the next stages, but take a deep breath and try not to rush into the future, when there's a lot to be done in the here and now. Make sure all documentation is ready for the interview, as some items, like police clearances and birth certificates, can take months to gather at times. Ensure all evidence is organized and ready for your visit to the embassy. Foster your relationship with your future spouse, keep it healthy, because the stress and anxiety will build and lessen at times, it has an ebb and flow. K1s are a true test of resolve to be committed. Always keep the love for your partner a priority.