How can mog offer to help pay for the wedding dress without offending anyone?

I think MOG should speak to the bride privately and just let her know that she thinks of her as a daughter and it would mean a lot to her if she could contribute to the dress. Make sure she knows that the contribution can be kept secret, and no one would need to know about it. She could also frame it as a wedding gift to the bride.
Another option could be to speak with the bridal consultants at the store she is trying dresses on at. She could discreetly let the consultant know that she is willing to contribute X amount of money towards the dress, so they can bring the bride dresses that fall within the budget of the bride’s contribution plus the MOG’s secret contribution.
I think it is really sweet MOG wants to help get her dream wedding dress 💕

Your mom would offer it to FSIL privately as a gift. It’s not a competition or shouldn't be. She can choose to tell her mom or not, at her own discretion.

I agree your mom should speak to the bride privately and ask if she can contribute to the dress and I d recommend giving a number of how much she wants to contribute so there is no confusion later. That’s very kind of your mom.

View Quoted Comment Thank you for the tips! I will definitely pass them along to her ❤️

View Quoted Comment Of course, definitely don’t want anything to come off as competitive. She’s just doesn’t want it to come off the wrong way

View Quoted Comment Thank you!! I appreciate the advice. Definitely a good idea to give a number

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All she can do Is make the offer. There's honestly nothing offensive about it, in fact it's a lovely gesture. FSIL can always say no if she wants to wear her mom's dress or her mom told her it would be her gift. In that case she can offer to add to the mom's budget without revealing the source. I wouldn't resort to secret deals with bridal consultants. There's no reason not to be honest. There's a good chance it that would backfire, and then it really would come off the wrong way.

This is all very sweet. One thing I would do is, when privately offering to pay for the dress, I’d include in the offer and make it clear the gift is for whatever she wants in a dress— so the gift would cover if she wanted a new dress OR alterations if she wanted to use her mom’s dress and “make it her own” — that way there’s no feeling like the gift is discouraging her from using her mom’s dress if that’s what she wants. I do think the idea of specifying a dollar amount is helpful.

View Quoted Comment Thank you everyone! FSIL found her perfect dress today! My mom offered to pay for the alterations as a gift but the bride’s grandmother said she was paying for them whether the bride liked it or not haha. I appreciate everyone’s feedback!