Good morning,
First off, no need to switch rites. A Catholic of any rite can attend another rites liturgy. Many in my parish are Latin Catholics who have been coming to liturgy for many, many years. Find an Eastern parish in your area and attend the liturgy and see what you think. Let us know how your experience was! No need to pick up a book and follow along, most of the responses are simple enough.
As far a switching rites, if that is something that your brother-in-law truly desires (again, there is no need to switch) he will have to live as part of the community for some time, maybe a year or so, and request a canonical transfer.
One thing to keep in mind, Eastern Catholics are not Roman Catholics with a different liturgy and more glamorous vestments. We are specific Churches with our own liturgies, theology, etc.
Wish you and your family the best of luck!
ZP