I think you need to stop and take a look at the new job opportunity and decide if that is something you see yourself being happy doing for the long term. While it is flattering to be asked take a moment to sit down with the practical. Figure out what your take home pay would be, the expenses you would have for childcare and see if the job still makes sense to you. As to the car can you use public transportation in the meantime meaning you can delay that expense or do you have a significant other that could take the bus and give you the car etc. Point here is to decide if you can make it work.

It does sound like you are seeing the current opportunity as something that is a one chance take it now or lose it forever thing and that may be one of the most important factors in the sense that if that falls into place then you can make the rest of it work out.

I think you are right in thinking that the timing is never going to be perfect and no matter when it happens you are going to have to make quick decisions and some that you would rather not make. I think it would be worse to return to your old job and then suddenly leave for a better job than it is to go from leave to a new job.