My Husband works full time and goes to school... he is always busy when he gets home. My kids, like any family, has their food preferences. Luckily, me and Hubby eat anything I cook. I cook whatever I know we ALL like. My son is super picky too... and he grazes throughout the day so I do NOT expect him to eat the majority of his intake at DINNER time, only. Because I know he eats fine throughout the day. So I don't "stress" about how much he eats at dinner. And what I think is a good amount of food, to HIM its too much. He will only eat until he is full. So that's fine. I serve him littler amounts. To fit him.
Next, no matter what my Hubby is working on... or even if just on the computer "relaxing"... He will come to dinner, with us, at the table. AND- I will tell him verbally a head's-up "Dinner is in 30 minutes..." so that he can finish up whatever it is he is working on... then he will come to the table. That is what we agreed on. We talked about it. So, try talking to your Husband about it. Openly.
Kids... need to "see" the "family" eating together. Ideally. It is a time to "connect" and talk story about the kids with the kids, and about us the adults. To catch up with each other or just hang out.
AND, for your picky eating daughter... encourage her to set the table and give her a head's-up on what you are cooking for dinner.. so that she can get it situated in her head "what" is for dinner... instead of coming to the table and then "surprise" seeing what is there and protesting. Tell her "This is what is for dinner...." "here is your plate... " and let her put on it what she wants FROM what you cook. And let her put whatever condiments on it (ie: ketchup) that she wants. Fine. It will give her some sense of it being her "own" food and choosing.
I would talk about it, with your Hubby. It is NOT an easy task... to be the corral "manager" for the entire family to get them to eat and at the table. HE should at least be making HIMSELF available, for dinner. That is his "responsibility" as an "Adult" and as a Dad. Dinner is just a short time, in the whole scheme of things... and making time for it is the least he could do. Because you the "Mommy" is not his "Mommy"...and he should be role-modeling "dinner time" for your kids TOO.
All the best,
Susan