I misread--the appeal is already a go. Ordinarily I'd suggest a routine round 1 appeal is no big deal, go do best you can--BUT I think if you were fired while under protecive FLMA or State coverage and your time line is not clear as you post it then the firm has a very big incentive to win the UC claim or get you to say something wrong at that level so it can then posture a big problem in contect of we didn't fire her--she quit. Were I in your shoes---I'd go into even this round with skilled counsel--the stakes are too high NOT to be using counsel.
Your post is very hard to follow as to time lines and you need to sort it out as to if you have a case under FMLA or CA equiv.
And its not clear from you post how your firm counts leave. The law does not require that firm permit linking various types of leave --but some firm do stack it up by policy, practice , or contract.
If you were at say week 11 of properly used FMLA and properly counted and expressed a need for 4 more weeks -- that would be more thanlaw requires and firm can demand otherwise politely or less soand if you go into week 13 you are dead meat to be fired for cause HOWEVER if the firm got it wrong and fired you in week 12 , firm got it wrong and very likley is going to have to eat it. Not the likley problem of your not being able/willing to work come week 13 is not material --you got fired wrong first.
But your need for leave must be inside the correct ballpark as necessary --and being a new mother is not a free get to stay home card --though it seems that way in many circles. "Bonding" is not something I'd consider a pressing medical need--but my views don't count--what counts is you double check that all your needs and steps fit within the rules to qualify for need.
Look I've been there when people requested time off to go home to try to get pregnant