We are both in similar financial positions. Given the will was clear on the 50/50 as someone said may blame that.
Don't 'blame' it on that or even suggest that you are - she will (legally quite rightly) say that, after receiving your share, you could hand it straight back to her for her kids.
I really don't see why you feel ashamed to take your inheritance - the same amount that she is getting. Suppose you worked in an old-fashioned workplace where they handed out envelopes with cash in on payday - would you feel guilty or in need of justifying saying "No!" if the next person in the queue, doing the exact same job for the exact same pay as you, turned and asked if they could have yours as well?
Her family has already had more money than yours, plus all of the presents and treats for the children (and maybe free childcare) provided by their DGM that your (as yet non-existent) children obviously never will.
She has absolutely no reason or justification for having the money other than that 'she would quite like it' - well, wouldn't we all! If she thinks that £400 isn't much money, she's quite at liberty to double her half from her own money and spend the lot on something nice for her kids; if she does see £400 as a significant amount of money, why on earth does she think that you should just give it to her?!
Also, as per PP, don't ever have it referred to as 'Mum's money' - and correct her if she calls it that. Don't let her kid you (or herself) that you're letting her/her family have a greater (well, whole) share of 'Mum's money'. It was Mum's money, but now it's yours, having come to you legally and morally indisputably yours - one of two children receiving 50% - it's now YOUR money. She is asking YOU to give HER children £400 of YOUR OWN money.
If you were to succumb and pay her £400 of your own money, on the shaky grounds that it was your share of the inheritance, be prepared for her to maybe start looking back at the whole inheritance. She might use the direct gifts to her DC as leverage and suggest that, instead of you two both having received almost half each and her children a much smaller amount, it would have been 'fairer' really for ALL the money to be shared equally between you two and the DGC - 'all of DGM's offspring' - so you 'should really' e-split it and give their family 'back' what 'should have' been their 'fair' share or - if you don't have it to give them, you're the unreasonable one and YOU owe THEM!!!