My husband and I stayed for 3 nights with our 1.5yo daughter and we had an amazing time! We stayed in the kid's wing on the 2nd floor. My daughter got her own bed and lots of welcome gifts. The room was so clean and had all of the amenities we needed. They had wonderful, thoughtful touches like kid's toiletries, robe and slippers, and a stool to access the sink/toilet. Housekeeping was very responsive and quick. We ordered room service and it was prompt and delicious.
Access to the hotel's amenities was all free when we stayed there. Unfortunately, the rooftop pool was closed for construction but the garden pool was lovely. Our room included the breakfast buffet. It was mostly Western and Korean/Chinese cuisines, and the variety didn't change much from day to day, but the food was very delicious! Great selection of pastries and the coffee bar was awesome. They also have a convenience store on-site with a seating area for dining.
My only recommendation is to have a car while staying here. The trek up the big hill to the hotel takes about 10 minutes and while it isn't terrible, it's tough after a long day. There are no bus stops on the hill, so you'd have to walk down to get to one. Once you're out of the grounds there are lots of shopping and restaurants nearby.
Overall, we had a wonderful time. The hotel is very kid-friendly and staff and guests alike are very understanding of the challenges of travelling with small children. The staff were very kind and helpful and were a huge part of why we enjoyed our stay so much. If we're ever back in Jeju I'd love to stay here again!