Isn't there a halifax account for children that you have to pay a regular sum into that pays a good rate.
The good thing about it in this instance is that after a year the money is swept from the high interest account into a regular halifax child saver account.
I assume that there is some sort of mechanism that the high interest monthly account could be paid into beyond a year, albeit the next year's issue with different interest rates.
It's something like you pay in a regular amount, up to £200/month (not sure of exact figure) and needs to be regular. Whilst each individual adult can only pay into one account for each child, each child can have several people paying into savings for him - so Baby Joe can have Mummy, Daddy, granny and nan-in-law all paying a regular sum each month. Mummy can pay for Baby Joe and Baby Jane, Daddy can pay for Baby Joe and Baby Jane, Granny can pay for Baby Joe and Baby Jane as well as Cousin Sue and Cousin Bob.
But if you could persuade her to set up an account like this, if you already had the halifax account set up (even with just a pound in) then the most she would ever get is a year's worth of the money going in. You would get the control of the main saving account (and could from there put it where you wanted).
On a separate note, have you asked her what would happen if her husband wanted to take out money from your dc's account if he wanted it, in exactly the same way he did to your dh? Would expect her to provide some sort of guarantee that he wouldn't.
Likewise, would speak to your nan in law and point out why you are so worried about your mil having control of the money and see if you can come to some sort of agreement that what your mil did to your dh was wrong, that you don't want that to happen to your dc especially given the form your mil has and especially don't want the NIL's money to go to MIL instead of kids therefore to give the money to you to save for them instead.
Finally - compromise might be to go to the bank together with your mil and the birth certificate - then when you are all at the bank, you can insist that you or dh are on the account instead of her - hopefully she will be too embarrassed to refuse - especially if you remind her of how worried you are about her husband deciding to use the money like he did with your OH's money - or if she does refuse then you can just apologise to the bank for wasting their time and say that you feel betrayed by your MIL and that it is obvious that she is just using the childrens accounts as tax dodges etc. You could even pre-warn the bank person setting up the account that this might be an issue and then you won't feel bad about it, they might be able to help.
And I think the birth certificate is a requirement for the money laundering laws these days - so whilst at one point you wouldn't have needed to show one, now you do...