LIN to MXP on a Sunday

Hello,
I'm booking flights and would like some transit advice. I will be flying in May to Milan on a Sunday, arriving noon from Frankfurt. I know Milan traffic is supposed to be bad. Is it better midday on Sunday? I'm hoping to make a 4pm flight to Olbia from MXP. I see there is a shuttle service from LIN to MXP. I will have a checked bag, will need to clear passport, retrieve bag and get to the shuttle, which leaves at 1:40. First question: is that enough time to make the shuttle, and second question: is the transit time 1:40 shuttle enough time to make my terminal 2 MXP departure at 4pm?
Thanks!