Next Tuesday is the biggest holiday in Korea that is, the first day of January in Tthe lunar calendar. Next Tuesday is the biggest holiday in Korea, the first day of January in the lunar calendar.

Next Tuesday is the biggest holiday in Korea, and that is the first day of January in The lunar calendar. Next Tuesday is the biggest holiday in Korea, and that is the first day of January in The lunar calendar.

Next Tuesday is the biggest holiday in Korea that is the first day of January in The lunar calend: on the Lunar calendar, it's the first day of the year. Next Tuesday is the biggest holiday in Korea: on the Lunar calendar, it's the first day of the year.

We generally say "on the calendar," not "in the calendar."

Next Tuesday is the biggest holiday in Korea that is: the first day of January ion Tthe lunar calendar. Next Tuesday is the biggest holiday in Korea: the first day of January on the lunar calendar.

Next Tuesday is the biggest holiday in Korea that is, the first day of January in Tthe lunar calendar, is the biggest holiday in Korea. Next Tuesday, the first day of January in the lunar calendar, is the biggest holiday in Korea.

Next Tuesday is the biggest holiday in Korea thatwhich is the first day of January in Tthe lunar calendar. Next Tuesday is the biggest holiday in Korea which is the first day of January in the lunar calendar.

Because of the pandemic, the government doesn’t recommend to gogoing to hometowns. Because of the pandemic, the government doesn’t recommend going to hometowns.

Because of the pandemic, the government doesn’t recommend to go togoing to your hometowns. Because of the pandemic, the government doesn’t recommend going to your hometown.

Because ofDue to the pandemic, the government doesn’t recommend to go to hometownsreturning to our hometowns for the holiday. Due to the pandemic, the government doesn’t recommend returning to our hometowns for the holiday.

Because of the pandemic, the government doesn’t recommend to go tohat people go to their hometowns. Because of the pandemic, the government doesn’t recommend that people go to their hometowns.

The most common way to express this idea, at least in American English, is to say "the government advises against traveling to see family over the holidays." Sticking closer to your original sentence, one always uses a possessive adjective when referring to a hometown: my hometown, their hometown(s), etc.

Because of the pandemic, the government doesn’t recommend to go toing back to your hometowns. Because of the pandemic, the government doesn’t recommend to going back to your hometown.

Because of the pandemic, the government doesn’t recommend to gogoing to hometowns. Because of the pandemic, the government doesn’t recommend going to hometowns.

However, my kids really wanted to meet their grand parents, so we finally cocame here. However, my kids really wanted to meet their grandparents, so we came here.

However, my kids really wanted to meet their grand parents, so we've finally come here. However, my kids really wanted to meet their grand parents, so we've finally come here.

However, my kids really want to meet their grand parents, so we are finally come heregoing back. However, my kids really want to meet their grandparents, so we are finally going back.

However, my kids really want to meet their grand parents, so we finally come here. However, my kids really want to meet their grandparents, so we finally come here.

However, my kids really wanted to meet their grand parents, so we finally come herewent back. However, my kids really wanted to meet their grandparents, so we finally went back.

However, my kids really want to meet their grand parents, so we finally coame here. However, my kids really want to meet their grandparents, so we finally came here.

We arehave been getting together and talking about our lives. We have been getting together and talking about our lives.

We are gettingplanning to get together and talking about our lives. We are planning to get together and talk about our lives.

You could also say "We will get together and talk about our lives," because you're talking about something will happen in the near future.

We are getting together and talking about our lives. We are getting together and talking about our lives.

"We are" is often said/written as "we're".

My kids also enjoy playing with dogs and cows in my hometown. My kids also enjoy playing with dogs and cows in my hometown.

My kids also enjoy wiseeing the dogs and cows in my hometown. My kids also enjoy seeing the dogs and cows in my hometown.

My kids also enjoy wiseeing the dogs and cows in my hometown. My kids also enjoy seeing the dogs and cows in my hometown.

You could use "visiting with" or "playing with" here as well.

My kids also enjoy wilike the dogs and cows in my hometown. My kids also like the dogs and cows in my hometown.

Other options: my kids also have fun with the dogs, have a good time with the dogs, enjoy playing with the dogs

My kids also enjoy withe dogs and cows in my hometown. My kids also enjoy the dogs and cows in my hometown.

My kids also enjoy withe dogs and cows in my hometown. My kids also enjoy the dogs and cows in my hometown.

We will stay here for three days here, and I hope my kids can havmake good memories. We will stay here for three days, and I hope my kids can make good memories.

We will stay here for three days here, and I hope my kids can havmake some good memories. We will stay here for three days, and I hope my kids can make some good memories.

We will stay here for three days here, and I hope my kids can havwill make good memories. We will stay here for three days, and I hope my kids will make good memories.

We will stay three days here, and I hope my kids can havwill have some good memories of their trip. We will stay three days here, and I hope my kids will have some good memories of their trip.

I'm not sure how to explain why you need to use "will" instead of "can" here, but "can" sounds odd to me as a native speaker. It's good to add "some" before "memories" to clarify that you mean "memories" in the sense of "recollections" rather than "the capacity to remember." Adding "of their trip" sounds more natural and also helps clarify that these are recollections rather than the capacity to remember.

We will stay three days here, and I hope my kids can havmake good memories. We will stay three days here, and I hope my kids can make good memories.

"We will" is often said/written as "we'll".