I'd be miffed if my DH didn't think that K was important. I think that is the biggest issue of all.
You and DF may need to have a conference with her teacher. Talk to him/her about what your DD is doing, why the homework and attendance is important, and what skills she is building for the other grades. Your school district probably also has a list of requirements for K, what they expect incoming kids to know and what they plan to teach them. Our parent handbook is right online.
When my DD was in a summer program, we had to miss a week. I asked for work for that week and DD and I sat down and did it. DH was surprised at how much DD was doing and at what level. Sight words, numbers, letters, basic math...It wasn't "hard". But she does need to do the work. My DD usually has one worksheet a day, and it's not much, and I don't do it FOR her, but I explain it and offer guidance if necessary. I can't tell my DD to "clean your room" without a little guidance. No way could she have done the packet without some specific direction.
If your DF doesn't understand the standardized pubic school system, then he needs to get educated on it. You can't just take a kid out of school for weeks. Not only is it detrimental to her learning, but you and he can be taken to court for truancy, or she can fail and be retained. I for one would not subject myself to court for a few days of goofing off, nor would I want my child to be held back because I couldn't understand the basic concept of compulsory attendance. If he understands nothing else, he needs to understand that unless he is willing (and CAPABLE) of homeschooling this child, he will only hurt her if he persists.
Kindergarten is a foundation. You are not wrong. If Kindergarten didn't matter, then we wouldn't bother mandating it.
Bottom line, kindergarten used to be a lot different than it is now. Your DF needs to get with the times or your DD will suffer for it.
ETA: I see other questions where your DF doesn't like structure. He doesn't see the need to sit down at the table for a family meal and learn manners, either. So you go on without him. I see this kindergarten thing as more of the same. If he doesn't get to just do his thing, he doesn't seem to see the value in it. I think this is a deep-rooted issue that you and he need to address, especially if you and he are to get married. Your children need a bit of structure. No so much that they are smothered, but most people get up, do something routine, go to bed and do it over again because that's how the wheels turn. If the household is at serious odds about that all the time, then it is ultimately detrimental. You can decide to ignore it, but it doesn't mean the conflict isn't there and won't erode the foundation of the relationship down the line. Perhaps what you and he also need is counseling to get on the same generic page when it comes to the structural needs of a family.