- I went to town in order to buy a new laptop and visit the Picasso exhibition.
the two verbs are in close proximity so repeating to is unnecessary. Now:
- I went to town in order to buy a new laptop for my daughter who will be starting college in a few weeks and visit the Picasso exhibition.
Here the two verbs are much further apart, in which case it is preferable to repeat the word to to avoid any possibility of momentary ambiguity. Repeating to signals to the reader that the first verb phrase is over and a second one is starting.
In the next sentence the two verbs are not very far apart but the first verb phrase is a coordinate with and:
- I went to town in order to buy a new laptop and a pack of DVDs and visit the Picasso exhibition.
In this case, too, it is preferable to repeat to in order to signal the start of the second verb phrase.
As to the OP's second sentence, the verbs are neither very far apart, nor is the first verb phrase coordinated, so there is little likelihood of ambiguity. But repeating to serves, in my opinion, to slightly emphasise that there are two purposes and to differentiate them (which is what I just did!)