That is very normal. But look on the bright side, they say that they are very seccure in your relationship to be able to seek others. :-) He still loves his mommy!
My two boys--who are 2 1/2 and 4 will ask everyday to see their Papa Carl--He and his wife provide my day care while at work--but there are times that the kids are at home with me and hubby we discpline them and they say "I want to go To Papa Carls" it is a way they get to go somewhere where the rules are different and things go more smoothly there. They do not do any work untilthe boys are gone--so they get undivided attention all day long--of course at home that doesn't always work. I do spend time with my boys and try to let most of the house work go and not worry about it-- or go home at my lunch hour and try and do some-so when we get home at night they have my total attention. Try and see if you can have hubby pitch in more around the house so that your little guy has fun one on one time with mom--not just the bed and bath routine---try and take him to a park and relax with him. See that you are going to get on his level and do crazy things with him. he will lighten up and start to go to you more with ease.
What you describe is pretty common. Both of my kids went thru phases when they showed a strong preference to either myself or my husband when they were infants and young toddlers. When their grandparents visited they would take to them and show a preference for them, they still do this in regards to their grandparents who live out-of-state. Of course, their grandparents provide extra amounts of attention and fun stuff. Don't worry about this its a phase and your son is much to young to form any lasting preferences at 13 months. Best wishes...