We never gave a crap about Christmas in SpermLand.  What the other kids at school get never even entered our minds.

I wouldn't waste the brain cell time thinking about any of this.  
 

Balancing what the blended family opposition does or does not do and what the parents of the other kids at school do or do t do seems to be a huge waste of time and concern.

IMHO

My first thought, BM will give SD an early christmas gift of a 3DS right before she leaves for your home. Hope I'm wrong. 

Stop trying to coordinate. She made your present worthless without the game system last year. Just do your own thing. 

We have a blended family, 2 of mine, 3 of DH's.  All are in their 50-60s now.  I felt it was important to have parity in our home so all Christmas gifts illustrated this.  Same number of gifts for each, same amount spent.  We do the same today including gkids and ggkids.

I disregarded what BM and my ex did.  So sometimes, the SKs ended up with more gifts than my kids because my ex was a deadbeat.  Thats life.  But my kids had stuff from their  grandparents whereas the SKs had no grandparents.  Thats life, too.

Our BM was very unreliable, ex was, too.  So I avoided any kind of coordination about gifts.  I wasn't even thinking about what outsiders, like other kids, would think, I had enough on my plate.  Besides, I don't think you can spoil kids with stuff, they are spoiled by letting them misbehave, just my opinion.

And we never even thought about what HCBM did.  So on years when we had Skids, we did Santa.  When they were with HCBM, Santa had already gone to Mom's, so it was just presents from us.

I think you are well meaning with what you are trying to do but there is no way you should be attempting to coordinate presents with a HC EX.

Just buy what you want and what you feel is appropriate for your home.  BM can do the same.  If you want to buy that game console.. buy it.  If BM also buys one?  then there is one at each home.. great for the kid...  That's the kind of thing that I would be unlikely to want to send to another home anyway.. to someone who is high conflict's control.

Like they others have said, there is no point in coordinating with BM, she has shown you how she is- believe her. 

Just do your own thing. 

In our family, the biggest thing came from parents and the other stuff all came from Santa. We used to try to spend equally in monitary but also in # of presents. Now that they are teenagers, we just do the best we can. BS tends to want electronics so he can burn up a budget with one gift, were as DD tends to want clothes so she will have much more. SS21 gets less than the other kids but stil has a good Christmas, but that is part of being an adult. SS16 only gets stuff if he shows up but I make his the same as my bios if possible.

Our HCBM loves to try to "coordinate" Christmas presents. In reality, she emails DH SS' Christmas list around mid-December (which always contains 25ish gifts) and then BM always says "Oh by the way, all the items have already been purchased by me, GF, BM or GF's parents, etc. but feel free to buy any of these for your house." Then DH has to find other gifts without a list. It's always a game of cat and mouse, so we have learned it's not worth it. We have learned to just do our own thing, even if it doesn't compete with BM.

Last year, I can guarantee that BM spent close to $3k on SS for Christmas, but she was doing it to overcompensate because DH and I had taken SS on a family vacation to Disney the year before. BM bought that kid a huge trampoline, skateboard, electric scooter, Nintendo Switch,  Xbox, and about 30 other toys. Like most kids, SS was thrilled on Christmas Day, but that excitement faded after the gifts were opened. A year later, SS doesn't play with any of it, so BM basically wasted her money. In our household, we prefer to do experiences (gift cards to the zoo, ice cream, museums, etc.), a scheduled family vacation, clothes, books, and maybe one hot ticket item per Christmas. We also see SS on a long distance schedule so it doesn't make sense to buy toys he may only play with a few times per year. 

I'm with the others, don't worry about what BM does, just do your own thing.  She won't believe in Santa much longer anyway. 

Speaking as a BM - Santa comes to wherever the kids wake up on Christmas morning. When the kids get old enough to put it together that it's not exactly the same, that's about the age they stop believing anyway. If they're smart, they will continue to pretend, so "he" keeps coming lol.

As soon as they started asking questions at their dad's, he stopped coming. They didn't push it at my house so he still comes despite them being 15 and 20! It's sort of a joke, though. When they get gifts for people, they get to "be Santa", and that can be fun too. When my son got older, he got to help be a tooth fairy for his sister. I promise, it won't mentally destroy them if everything isn't perfect. 

Um. What? Do you have a good relationship with bm where you guys can coordinate effectively?  I would say no.

You do your thing and she does her thing. You can't tell bm not to get her own daughter something. You can let bm know your plans but don't be surprised if bm gives it to daughter first just to spite you. We spoil the heck out of our kids at Christmas but we also donate to families in need. Worrying about other kids at the school should not be a burden your children should have to bear. Let them be excited about their presents. The political correctness of this post is a lite much. And don't control bm's present giving. If you want to get the girl a ds then do it. It's not a competition.

Buy what you want. Please just buy what you want. Dont go for broke, ok?

Our bm bought everything WE told her we were buying for our house. Since the skids alway's had Xmas Eve and Morning with bm, the kids opened present after present saying OH we got this at home, WE got this at our house.

We thought we were being thoughtful by telling her the Santa list for our house....Money was very tight for us then. First we thought it was a coincidence. I never thought, WE never thought, anyone would be so darn cruel. Until, the next year it happened again.

It was the 2nd time we knew she did it on purpose. What an awful woman to do this to her kids and us. THAT was just the beginning.

When the kids were older...they did the same thing to us. OH Thumper I would love to have this for Christmas. So, I bought it. It was close to 100.00 in cost for 1 thing.

Guess what? BM bought skid one too. Worst part is skid told his dad,  OH I lost yours, glad my mom got me one.

Just buy what you want op.

2 separate homes with 2 separate dynamics.

Naïveté is painful.  Make your self learning curve as steep and short as possible.  The most painful road in blended family land is paved with good intentions.

As for the kids at school....  advantaged, privileged, entitled, and deserved are the most destructive and dangerous concepts in modern western society IMHO.  Earned, worked for, accomplished, created, etc  are the powerful and positive side  of that coin.

I have never heard of a single incident where what a kid got from Santa caused a problem at school.  Don't create drama where none exists.

IMHO of course,.