My boy is turning 2. Is it appropriate to invite 13 year olds to his birthday parties? We argue a lot about this.
At two years old, I'm assuming that the party is mostly a get-together of parents of small children (most 2-year olds aren't at the stage where they have their own social circle). The main problem with inviting a teenager or near-teen is that it is unlikely that his/her friends will be there, and thus he/she will be left out, and basically have nothing to do for the entire party.
This won't be fair to the teenager, and it could make the party extremely uncomfortable.
On the other hand, if the teenager wants to be there, (e.g. because he/she's close to your child), I'd make sure that you're doing something they can be involved in, (e.g. party games like charades) and if at all possible get some of his/her friends round, so he/she won't be so excluded.
Certainly, the most important point to remember is that from the perspective of the children, a two-year old and a 13-year old are completely different. The older one might take care of the younger one, but they're not friends.
When we have done family parties we had children of all ages, so long as we had something for them all to do, or they had someone their own age or near to be with - things were fine. For my sons first year parties they were all for the family rather then the kids, the second birthday party was more about them but we still had mostly the family.
If the 13 year old is someone related, you don't really note the relation, then being with the family might be enough - or be nice and let them bring a friend along.
Until the children get older and have their own friends or classmates they want to be with I've never seen limits on ages, especially when considering family members.
I just invited a seventeen year old to my daughter's six year party (he is really important to her, a good influence, baby sits and is involved in the same theater group as she, plus his parents are friends of ours).
However, I asked him to take on a role in the party and provide some of the entertainment. It gave him something to do that engaged his strengths (as a drama buff he loves entertaining and put on a magic show), honored the difference in age (he also was given a "thank you gift" instead of a "goody bag") and placed him in the role he is for Alice, mentor.
Kids need people in their lives from a variety of ages because this provides them with a maximum amount of opportunities for good socialization. The fact that this young man is being considered by you in the first place causes me to think he is important in your family's set of relationships and probably important to your child, not to mention an accepted and appreciated influence.