Sonja Prokopec took her son on their first "solo" trip together when he was six years old.

They went to Rome, and it was so memorable that Prokopec said she's now planning their second trip this summer.

"I really enjoy one-on-one time which we have when travelling alone," she said. "There are no distractions, no arguments among the siblings, time spent together is of high quality... My son still talks about our time in Rome and can't wait for [our] London trip this June."

Prokopec and her husband have three children — her son who is now 10, plus two younger daughters. They travel together, but time away with just one child and one parent has perks that family trips don't often provide, she said.

"Travelling with only one child allows you to focus on the needs of only that child," she said.  "Also, as I am not stretched from managing different demands, I feel like I am a better parent — more patient, more playful and more in the moment."

Plus, "my son loves all the attention and loves that we get to explore together, just the two of us," she said.

Prokopec's husband — who "always insisted on doing things together, including travelling" — is now a proponent too, she said.

"My husband has also taken my son alone to Turkey and really loved it … even he sees the value in it," she told CNBC Travel.

Prokopec hasn't taken solo trips with her two youngest children, mostly because of Covid-19, she said. But that may soon change.

"I will definitely do more," she said.

A growing trend

The luxury travel company Scott Dunn named "parent-child bonding holidays" one of 2023's top travel trends.

Mother-and-daughter trips in particular are on the rise, though father-and-child trips are also becoming more popular, according to the company.

"Parent-child duos often pick destinations and include experiences based on their mutual interests," said Scott Dunn's General Manager Mike Harlow.

Harlow said his company recently helped a father-son duo book a trip to Cambodia that focused on the country's history and national parks.

"We also had a mother-daughter duo who headed to South Korea for a trip themed around K- dramas and K-pop, while another mother-son duo travelled to India to do the classic Golden Triangle together," he said.

Elephants and 'jungle bubbles'

Last year, I decided to book my own mother-daughter trip with my oldest child. (To satisfy cries of injustice from her younger siblings, I promised everyone a "solo" trip at their 10th birthday, too.)

To decide where to go, I asked my daughter a series of simple questions: beach or mountains, cold or warm weather, animals or adventure sports?

Based on her answers, I presented her with a few ideas. She chose the Anantara Golden Triangle Elephant Camp & Resort, outside of Chiang Rai, Thailand. We booked several nights in the main hotel, and one night in the hotel's "Jungle Bubble" — a spherical tent with a king-sized bed and bathroom that overlooks part of the hotel's 168-acre area where its elephants can roam.

By day, we walked with the elephants through the fields and watched them bathe in a river along the Myanmar border. We prepared food for the elephants and fed them, but we did not ride them, a practice that is neither allowed by the hotel nor condoned by animal rights supporters.

In the evenings, we swam in the hotel's pool and held a "spa night" in our room, with facial masks from home and bath salts and lotions from the hotel. At night, we sat outside and looked at the stars.

One morning, I suggested we book a cooking class. But my daughter was adamant about trying Muay Thai boxing instead. Resisting the urge to tell her she wouldn't like it (read: I wouldn't like it), I booked a session. She loved every minute.

As for me, I cherished having so much time with my daughter, without having to tend to others' needs. I found myself telling her stories from the past — my own and my husband's — simply because, without competing voices around, I could.

The time also afforded many teachable moments — lessons that had long needed to be taught. While resting in our room one day, I suddenly remembered that we needed to place lunch orders for my daughter's next school term.

"Mom," she said, looking up from her book. "We can do that when we get home."

As a bonus, my husband reported having a wonderful time at home with my other children — enjoying their own special moments as a trio, without the complications that can come with a family of five.

Memories that last 'forever'

California native Madeline Austin also grew up with five people in her family. She said she vividly remembers the trips she took as a child with her mother and grandmother.

The trips "centered around something they knew I was interested in. For example, I did a report on Yellowstone National Park in elementary school and became obsessed with the geysers, so they took me on a long weekend trip to visit and see them in real life," she said.

Austin said her family didn't travel often, so it felt "incredibly special" to take trips with her mom.

"She was invested in my interests, and the undivided attention I received from her that weekend — especially as the forgotten middle child — was truly special and something I'll remember forever," she said.

She recalled holding hands with her mom and watching a geyser erupt. "I also remember leaving the park tired from walking, getting dinner together and being able to order soda — which we didn't usually have at home!"

Austin, 27, isn't a parent yet, but she said she would continue the tradition with her own children one day.

"It's such a special time to connect one-on-one with your child in a way that you can't replicate at home."