PSW Dependant (Baby's visa and UK birth certificate.)

[jasmin]

Hello

My husband is a PSW holder and I have dependant visa already.
Our baby boy was born in UK last year and recently brought him to my home country Japan.
So what I need to do now is apply for my baby's entry clearance in Japan to go back to UK & I have some questions..

I'm going to submit my baby's UK birth certificate as proof of relationship with the main applicant(my husband). But is it enough? Do I also need to submit our marriage certificate again?

And When I was looking at UK birth certificate(long one), I noticed there's no information of parents' date of birth, only names/nationality & occupation and started wondering if this is ok enough..

If anyone who has applied baby's visa only and knows about this, please help..!