It will not be weird or strange unless you make it that way. There are sooo many families like this at our daughters schools and my niece and nephews schools. Some of the couples are just cordial with each other and some are pretty close.
I always try to congratulate them on putting their children first and trying to make every thing amicable. .
I am a child of divorce and it was AWFUL. I still have nightmares and memories of the screaming, the uncomfortable gatherings, hand offs.. Events..
If you all will make an agreement to respect each others space it can make you all feel more comfortable.
My sister and her ex, trade off weeks. Their homes are less than a mile from each other. The kids have their things at both houses. But the kids are responsible for making sure whatever they need or want is taken to the other house so there is not a lot of running back and forth. Of course there are times when the kids will need to go back to their other house and get something. When a child is at their home with their dad, they follow his rules and are there for that whole week. No running back and forth, no drop ins by the other parents. They are of course allowed to call their mom, but they are living in that house for that week. That parent makes the decisions for that week. Sleepovers, field trips, they are responsible for that weeks transportation to sporting events or school obligations. Of course there are phone calls made to trade or ask for help etc.
Yes, they run into each other (grocery store, gas stations, neighborhood eateries), but are polite. If the kids are with one parent of course they still greet the other parent naturally.
They do not eat together at restaurants if they run into each other... But I do know many divorced families that after an event they will all agree to meet at a neighborhood place with the kids.
My sister does date. Her boyfriend will go to the sporting events or performances of the kids with my sister. Everybody is polite, but they are not friends and so not even sit together.
In the beginning my sister and her ex had to have 2 separate conferences with the teachers because the refused to go together, but after a few years realized it was not fair to the teacher. and now they either both go or one goes and then updates the other on what was said.
It is better but not perfect. My BIL's wife is very nice. They have a baby together now and it is my sister who has a problem with them.. But I really admire and am thankful about the new wife. She is kind and loving to my niece and nephew and has always been gracious to our family.. She is the mother of my niece and nephews baby sister. She will always be part of our lives. My sister is just immature (even though she is the one that wanted the divorce) I have had to apologize for her behavior so many times. But that is a whole other subject.
Just keep in mind you all are doing a great job of making the children's lives easier. They will realize this at some point.