DD has a Boxing Day birthday.
The years that we travel "down home", either DGM hosts (if we are staying in one of our childhood homes) or we host (if we have been sensible enough early enough in the year to rent a cottage for the break) a party of sorts for whatever family are around.
DBIL's family used to have DSILs family gathering that day, a couple of hours away, so could only call in for a few minutes as they hit the road. DSIL lives a couple of hours away and is rarely home for Christmas herself (with DH and DCs). Half of my DSiblings are away and don't come "home" for Christmas, more so since their DCs arrived. My family only come quite late after the "traditional" long walk, and DPs/DPILs (well, the 2 DGMs really) don't get on so it's always a little tense (fraught!).
The years that we don't travel, we host a gathering at home. Our families don't tend to come, very occasionally a couple of them have, but mostly not. There are some extended family (DAunts and DUncles) of both DH and I living relatively near us, but they also tend to be too busy to come.
But we have a lovely road and great neighbours, so it is a great excuse for us to relax post-Christmas. We light the fire and get in a load of M&S party food, and put on mulled wine to simmer. Different people call during the afternoon, some stay a half an hour, some only go home in the early hours of 27th....and it's relaxed, they can all walk home, and can come to us after their family commitments. And DD's friend up the road comes after visiting "Grammaw" so they get some time together too.
We do a "proper party" for DD's friends at a time that works for DD. It would never work over the Christmas holidays - everyone round here is way too busy with family and travel, and needing a break from activities. So it was often the 1st Saturday after going back to school in January. But if she wants to do outdoor or adventure things, we have a party later in the year to make it enjoyable (eg. climbing wall in March, sailing in June) or we've done a "back to school sailing party" at the end of August another time, with pizza etc after getting dried off instead of a birthday party another year.
The only thing we've ALWAYS done on the day is a birthday cake - which might be just DH and I with DD. We usually buy it in M&S on Christmas Eve, rather than making it ourselves on 26th (we bake at other times - and occasionally have for her birthday - but I really prefer not to HAVE to) and she gets to choose it. Presents from people other than DH and I can happen on the day (if we've been given them in advance or we see the givers on the day) or anytime afterwards that we see them. Which can be a nice way of spreading them out a little.
But in terms of having a separate event for DPs/DPILs not on the actual day, absolutely why not?! As long as you designate it in advance and they all know which day, then being able to do Christmas and all that entails, but get a little break after it before the birthday and hosting or even managing one DM hosting the other DM and all the passive-aggressiveness that can go with that, sounds like a good idea!