I hate it when people bank cheques late because it always catches you by surprise. If she is on a tight budget a $40 cheque being cashed without warning could overdraw her account or get bounced which could cost her extra fees and if it's bounced some embarrassment as well.
I think that although it's rude not to accept a present it would be ruder to cash a cheque without warning.
Maybe you could write her a thank-you note saying that you were so rushed at the time with a new baby that you put the card and cheque and aside and you only just found it again now. That way she would have some warning of your intentions. Of course if you've aready sent your thank-you note that wouldn't work.