That is not a clear "we are going out of town." Instead of going out of town, do something in town or reasonably near by. A night or two in a nice hotel/spa,room service breakfasts in bed, walks to great lunch places near by,  foody dinners each night at nice restaurants, drinks and dancing after dinner, etc... You can do much of the prep for your Easter gathering before you toss your LBD, heels, fun stuff filled overnight bag, and DH in the car to go for a one or two night resort fest in your city.

TMI is never a good idea with these types, the ones like your MIL, with their meddling and overstepping.  What they don't know, is far more difficult for them to manipulate or interfere with.

Get creative, provide near zero information, and enjoy your life.  Take DH's phone when you get to your hotel, shut it off, and toss it in a drawer not allowing him to touch it until you are back home and he has helped you with the Easter prep and set up.

Control how much wallowing he can do with his mother, X, and the noxious spawn. Make your own life easier.

With this strategy, if MIL gets BM to surrender SD-15, that will be irrelevant to you and DH as you will be doing what you planned.  If MIL, BM, and SD lose their minds that you two were not there for them to leech on to DH's B-day celebration, tuff shit.

We did this in Dec.  Not for a celebration or to keep anyone in their place.  We spent a week in a resort in our city. DW worked at her office during the day, we did meals, shows, shopping at night. While she was at work, I drove home and did the pre-guest deep clean of our place in preparation for my parents and my aunt coming for Christmas and mom's 80th B-day.  We checked out our last AM, she went to work, I went home, and my parents showed up mid afternoon.  It worked like a charm.

There is no need to share shit for anything with MIL, BM, or the noxious spawn. 

So don't.

Have fun.

Your MIL's lack of social/situational awareness is either astounding, or she's faking it on purpose. You don't "surprise" people who are basically estranged by having one of them show up at the other's birthday. Geez. That's called "blindsiding", not "surprising." 

they wanted to surprise DH by getting SD to make a appearance.

So, this is not something that SD necessarily wants to do, just something MIL wants to stick her nose into and orchestrate. No, thanks.

I mean, how awkward for both SD and your husband (and everybody watching). What is wrong with your MIL? Somehow, you need to politely tell her to stay in her lane. If she wants to help, she can have a conversation with her granddaughter about respect and how one should treat ones parents.

Where do they want SD to make the surprise.. at your family easter dinner??? or at your getaway night? weird.

"That won't work for us."

MIL needs to keep her nose out of it. Is MIL invited to the event you and your sister are co-hosting? If not, she's got a lot of nerve inviting herself and and SD. Even if she is, she's got a lot of damn nerve inviting SD without clearing it with you first. Where's my broom? I'll give her a solid smack on her meddling arse.

She's doing what she wants with no consequences for herself. But making life difficult for you. I would not get involved with BM.  If the CO has Easter as your holiday. Then expect SD without asking her.  If CO said  it's BM holiday. SD  will be with BM.

Personally I would rather spend my holiday at McDonald with DH. Then get involved with this crazy family.  O.K applebee they have a bar. 

MIL does not need to know the details of your weekend. Just tell her you will be out of town, even if you won't be gone the whole weekend. If she wants to have a party for DH and invite SD, she can do so on another weekend.