do parents and their kids always have the same DNA?
In case of asexual reproduction, the offsprings are genetically and morphologically identical to their parents, so they have same DNA. In sexual reproduction, parents and their children don’t have same DNA but similar DNA as the child receives DNA (or genes) from it’s both parents.
For e.g. in case of humans, each cell normally has 23 pair of chromosomes (total 46). Twenty-two of these pairs, called autosomes, look the same in both males and females. The 23rd pair, the sex chromosomes, differ between males and females. Females have two copies of X chromosome, while males have one X and one Y chromosome. Each parent gives a kid one chromosome from each pair so a kid has two copies of every gene from both the parents. Therefore, kid will have parts of both the mother and father's genes as a unique sequence. That's why no single individual has the exact same DNA sequence as anyone else.