the Allens being friends with the Morlands and childless, they may have a good relationship with the Morland children (which they seem to have, actually), and they may give them presents and sweets from time to time, the kind of thing an uncle and aunt would do.

They had already planned to go to Bath, and bringing someone else with them would not be too great an expense. Catehrine had the right age to do that kind of trip, and as you pointed out, Catherine's mother would not have the means to introduce her iun a greater society.