My advice:
Try to be careful not to be fired for X or Y during the "new" probation period, and make sure the new company is safe...

I had people I new from old company who finally found better, to get fired 1-2 months after because of the crisis... and they had to come back to the **** old company (which is not always possible)

I think if you're happy here and have a future in your job, maybe you should stay...

Or better if you are "safe" (like you can't be fired easily, etc...) talk to your manager and let him know you think it's time to get a raise, your family situation changed, your valuable, blablabla.