Ask about willingness before counting on help
A relative might enjoy doing one school pickup but not have time for every Tuesday. Ask a question that describes the actual responsibility: which days, how many weeks, what time, and what the person must do if the school schedule changes. Give them a chance to accept some dates or decline entirely. A general expression of interest is useful information, but it does not fill a specific gap in the calendar.
Avoid announcing a plan before the affected person answers
Give them a way to decline without undoing a plan already announced. Present the options, the likely commitment, and the deadline. If they decline, return to the original decision rather than telling them the household has already counted on them.
Build the arrangement around the answer you receive
If the relative can cover the first two Tuesdays only, record those two dates as confirmed and leave the remaining ones open. Agree who can contact them about a change and what notice they need. If their answer is no, thank them and continue planning without suggesting they have disrupted an already settled arrangement. Before asking again next term, check their current circumstances rather than carrying their past acceptance forward indefinitely.