UK Indefinite Leave to Remain for mother of British baby?

My wife is Korean, I am british, and our 5-month old daughter is british (with british pport). My wife has applied for indefinite leave to remain in the UK as her 2-year spouse visa is about to expire, but we were in Korea for 8 months to have the baby and we didn't have much evidence we were together during that time. If her application fails, will she be separated from me and our baby? Our baby is 100% -fed and completely dependant on her, it seems unfair. The baby and I would be forced to follow. Would we have good grounds to appeal?