How can parents explain to young children that this is not rejection, nor lack of love? It is just that parents sometimes need time off, alone, without being contacted through any means.
Surely by now you have successfully gone to the bathroom without someone pounding on the door and asking "What are you doing in there?" - your solution to this situation is like that, but on a slightly larger scale.
If you want to be "off duty" in the early evening, now that they're staying up later, you can use just that wording. You could decree that after 9pm you won't be getting snacks, reading stories, or anything else non urgent. You'll be in your room reading or working or watching TV. They can be in their rooms or somewhere quiet but they should leave you in peace.
If you want to go away for a week or two vacation, and not even be contacted in that time, you will have to work up to it. Perhaps start with an overnight trip. (Your question is unclear about just how much alone time you need and whether both parents need it at once, or by turns.) You can establish what the norms are in your family and how frequently you need to be away from your children, and for how long. Emphasize the positives such as who will be with them instead. You don't need to tell them "I need to be alone" or "I need time off." Instead use the same tone as you would for a business trip or "family business" such as visiting a sick relative. "We need to go away for four days and X will be staying here with you. We won't be able to talk on the phone as much as usual but I'm looking forward to hearing all about the fun you had when we get back!"
Some people will tell you that you don't actually need alone time, at least not much longer than it takes to use the bathroom. I'm not going to argue with you about it. I went on plenty of trips without my kids, leaving their other parent at home with them. I went on plenty with them, too. I didn't feel the need for time without them myself. That doesn't matter though: this is your family. I will warn you that if you discuss this with your children using words like "rejection" and phrases like "lack of love" you will introduce a germ of an idea to them that probably wasn't there before. If you need to be alone, be alone. Just don't protest too much about why. I doubt you would discuss with them the details of which clients are important enough to need a visit, or why you chose to speak at a particular event, or the details of Aunt Susan's surgery, so take the same approach with your need for alone-ness.