No problem at all. Checked bags on regional jets works the same way as on mainline.

To clarify the gate-checked bag process, it's helpful to know that regional jets (even the 700s and 900s) have smaller-than-mainline overhead bins. As a result, the airlines have developed gate-checked bags to allow carryon bags that meet the normal size requirements to be put in the cargo hold on regional jets, when those bags don't fit.

So, as your family is traveling, if you have any large (but legal!) carryons, you can get a pink tag at the gate before you board the regional jet. On your way down the jetway, you can drop your bag off at a designated location (often at the end of the jetway). The bags get taken and loaded into the cargo hold of the plane. After the flight, you'll wait somewhere (usually the jetway, but sometimes outside the jetway) and pick the bags up again. Occasionally, some airports will take all gate-checked luggage and take it to the baggage claim--from what I've seen it's not overly common, but it happens.

Happy travels!