Rarely do kids have parties on their actual birthdays because you need a weekend or day off. I'd schedule a party for each kid a week or two apart, but do an immediate family dinner and cake/gifts on the day-of.

My family and also DH's family usually do combined birthday parties at the grandparents' homes, to make it easier on everyone to get together. But we do individual celebrations for each kid within the immediate family and neighborhood.
Is some compromise like that an option for you?

I would not combine them!!!! Efff that....

Better yet....have your DDs party when SD is with BM!

You do whatever you want it. The only reason I'd do a combined party is to save money and bc I want to not bc family expects accommodate skid. 

They aren't twins! Remind your DH that birthdays are that persons individual special day. I can understand family and DH wanting to combine, probably to cut down on cost and need to have two parties so close together, but what happens should you have another child down the line, whose birthday doesn't happen to be in July? That child will get their own party, where the two girls will have to share theirs...that just sets up for the future of breeding resentment and hostility between the siblings.

For extended family parties,  I can understand the desire to combine birthdays that are close together.  It's a hassle (not to mention expensive) to entertain twice in just a few days,  and it can be inconvenient for guests to come twice in a week or so. I would be ok with a shared party, provided that each child got a cake and special celebration with the immediate family on or close to the actual birthday. 

However, "special" birthdays, such as a first birthday, or a 16th, or whatever is special in a given family,  call for a separate party if parent or child wants one.  I can't imagine, as a new mom, sharing my child's first birthday party, with the fun of watching baby with a smash cake and the wonderment of the birthday child, with a stepchild. 

I wouldn't be combining the parties.

In my immediate family growing up we have Dec 23, Dec 27, Jan 3 and Jan 13 - PLUS Christmas in there. We still celebrate everyone individually. It is a lot, but we don't believe in lumping people together. 

No reason for your family to be at SD party.  No reason for SD in-laws to be at your DD party.  Do not let in-laws control your house.  Not fair to your DD.  There going to be many years of birthdays , special events,  each child should getbtherr own day in the spotlight.  They are trying to make life easier for THEM at your DD expence 

Parties for a 1 yo are not for the kid.. they are for the parents.  Just my opinion that babies don't have much tolerance for big celebrations and certainly won't remember much of it anyway.. if anything.  If you have one it's because mom and dad want cute pictures and to celebrate with family.

parties for a 4 yo... are actually starting to get to the point where they ARE for the kid.  The kid understands the hoopla is for them.. that they will get presents and cake etc.. 

Now, lots will depend upon the dynamics of the families involved.  If it's close knit and nearby relatives.. it's easier to do more than one celebration.  If it's an effort for people to make it then it's asking a lot to have more than one party for people to attend.  Of course we have the covid issue too.. and how many relatives exactly are we talking about???/  that might be a reason to split the parties in some cases to reduce guest list..

I can get that it would be tough to share a 1 and 4 yo party because the 1 yo party is more about curating pictures with the baby.. smash the cake etc.. the older child will be all.. presents.. presents.. presents.. GAMES.. we need pin the tail etc.. 

It would be different if the kids were really close in age. .but the things that people would do is different.

I do like the possible solution of letting his family have a "joint celebration of sorts" but still do your own separate celebrations for both kids.

I would absolutely NEVER even consider a joint birthday party CERTAINLY not for my DD 1st birthday. Can she be special for her day by herself? Lol your DH and in laws are crazy

Do them separate.