There are two celebrations here - your DD's birthday and Mothers' Day? Which one means more to you?
Personally, I wouldn't be comfortable having a meal with my ex, so I'd decline politely. Not seeing my children on Mothers' Day doesn't bother me. They've always sent me cards and gifts and usually rung me, so that's fine.
As far as my daughter's birthday is concerned, I rarely see her on the day. She lives 200 miles away, she usually has to work and her preference is to go out with friends. Of course, I send her a card and a gift (usually money) and I ring her (or text if she's unavailable). Not having personal contact on the specified days has never bothered me.
This year has been a bit different. My own birthday is just after Mother's Day and it's a milestone birthday. My daughter and son have arranged for a meal in a nice restaurant in between where my partner lives and her own home (location was my request).
Obviously, my partner is invited and he has arranged for us to stay overnight after the meal in a hotel, as part of my birthday present. I was looking forward to it because I so rarely see my children (especially together) and the hotel is in a picturesque part of the country and I was looking forward to a walk before heading home.
My partner has known about the plan for ages, so I was quite upset when he announced that he intended to see his own mother on Mother's Day, which would have meant that we would have driven another 100 miles and not been able to relax on the day after the meal. It spoilt the weekend for me. My feeling was that he hadn't considered me when he came up with his plan to visit his mother, whom he does see quite often. I confess I was grumpy, but I was determined not to let it ruin the meal.
Anyway, it's all been sorted now. It turned out that one of my partner's siblings was taking their mother out. He couldn't find anywhere that wasn't booked anyway. He's going to see her on another day and is taking her out for a special tea - so all's well that ends well.
Nevertheless, it has been an example of how complicated families and commitments/expectations can be. I don't really expect much from my children, although I'm always delighted when they do go out of their way to do something special. We're very close. Being able to natter about just about anything on any day of the year is far more important to me than feeling obliged to celebrate on specific days.