。
She's planning to visit her mother next Tuesday.
Literal
She [topic-は] next [possessive-の] Tuesday [on-に] mother [object-を] visit intend [is-です].
~つもりです ('intend to, plan to') is the standard frame for stated intentions — sits between the casual ~ようと思う and the more committed ~予定 ('have a plan to'). The に here marks the day, parallel to 月曜日に, 三時に (specific points in time). 訪ねる (たずねる) means 'to visit (a person)' — distinct from the homonym 尋ねる (also たずねる) meaning 'to ask, inquire about.' Both share the kun reading, distinguished by kanji and context. Days of the week each get a specific kanji ending in 曜日: 月曜日, 火曜日, 水曜日, 木曜日, 金曜日, 土曜日, 日曜日.