Lesotho can be a welcoming destination for children, though the rugged terrain and conditions are better suited to older children who would enjoy hiking or pony trekking. Most pony trekking centres arrange treks only for people over 12 years old.
Be aware that everything is rougher around the edges than in many parts of South Africa. If you (and your children) are of an adventurous bent, you'll likely find travel here enjoyable. A little advance planning is recommended because some accommodation options, such as the trading post lodges, are family friendly while others are less helpful and comfortable. Discounted accommodation rates for children are common.
Informal childcare arrangements can be made; if you are staying in a good lodge or hotel, staff may be able to assist.
There are reasonable medical facilities in Maseru, but for anything serious you'll need to head to South Africa.
Nappies, powdered milk and baby food are available in Maseru, with only a limited selection in smaller towns.