Sorry, this got long.
Border collies are smart, if they had opposable thumbs we would all be in trouble. Definitely smart enough to learn to leave food that falls to the floor alone. Mine does, and she is a breed that lives for food. And in 2 years, when the kids are not dropping food on the floor, will the dog still be in exile for meals? Dogs are social/pack animals, they like to do things together, especially eating. For your dog, together means with you.
If you are having to make all these adjustments for a well-behaved 5 year old dog, Cassie is right, this is probably your last dog. Your SO does not sound like someone who will be able to cope with either house-training and otherwise training a puppy, or adjusting to an older foster dog who is having to adjust to the household. In fact, if he doesn't like having a dog around at 5, wait until the dog is old and having health issues. There will be complaints. I've seen families where the kids and one parent loved the dog, and the other parent didn't - there were definitely issues in those families. And that was when the dog came into a family (parents and children), not when the dog was part of the ingredients of a blended family.
So far he is OK with the cats? Once there is less dog presence, he may start to think that some of the issues he thought were dog issues are also cat issues. I loved all my cats dearly, but now that I am cat-less (age takes us all, including my cats) I sure don't miss the kitty litter tracked several feet, or cleaning the litter box, or finding the wet icky hairballs in the morning. My cat could throw up discretely, whereas the rare time the dog does it can be heard all through the house, including at 3AM. A pain, but at least I know I have something to clean up now, instead of finding surprises later.
From over here, this sounds like a potential room-mate situation for incompatible room-mates. Unless there are overwhelming reasons to move in together (and I am having a super hard time thinking of any), your relationship may be better if you are two households. After all, the food your dog is scarfing off the floor is coming from his messy unhygienic kids. Three and five year olds should not be adding to the dog's diet that much. One year olds, sure, but not three. How come they are such sloppy eaters? And when they are sick, will he get up and wash the sheets and remake the beds and all those other icky aspects of childcare, or will he expect you to? Or when they hurl on the nice wood floors, or get hurt and bleed all over the sofa or car, what then? (Sorry, my parenting memories just surfaced, nothing there any parent has not had to deal with).
I guess all my biases are showing - I am definitely a "love me, like my pets" kind of person. I like having the dog on the bed (in winter, we are both happier that she sleeps in the bathroom on a cold tile floor in summer, her choice), I like hearing her quietly breathe as she lies on the floor behind me right now.