All I can think of is you taking a nice stroll through the park, occasionally sit and relax while enjoying the sights, as you essentially eliminated everything else. Oh, and there is shopping at the gift shops as well.
However, is there anything in particular you want to ride? I know you said your DH is taking the older one's on rides, but if you truly desire to go on any of the rides you can do child swap. I just do not want you to completely eliminate the idea of you enjoying any rides at all if there really is anything you're interested in.
One ride I realized you can do with your baby, by yourself, is the Hogwarts Express (taking off from Hogsmeade is one experience, taking off from Diagon Alley is a different experience), but that is only if your family is planning to do park-to-park tickets.
EDIT: I just looked up Caro-Seuss-el and One Fish, Two Fish, Red Fish, Blue Fish and both have no height requirement. However, if you're worried about your child moving (as you mentioned before) HE might be the best ride for you.
Also, I know you said maybe not shows, but you can at least try to do shows that are outside and sit in the first seat in rows closest to exits, that way if your child moves too much, or starts crying you can make a quick escape without disturbing people. There are a few inside shows (with moving seats) that have seats that do not move and you're able to enjoy with a baby, but since you seem concerned about you not being able to do shows at all, I would recommend an outside show if you change your mind on even wanting to consider trying.
That being said, if you do not want to ride anything, or do not want to consider shows, especially if you do not want to do play areas, I honestly say that it might even be better for you to not go into the park at all. I feel it seems pricey for someone to have to pay the amount of money you'd have to do for you to simply enjoy the sights, as you can easily shop at the City Walk and if your family wanted to enjoy lunch, or dinner as a family they could leave the park and meet you at a restaurant in City Walk.
However, I have to say if you love taking photos, just walking around and taking as many photos as possible to capture all the sights would take some time and fun (at least I personally love taking photos), especially if you might decide to hang around your family and would like to take some candid shots before and after their experiences. As they're on the ride, you can take photos of the area, or shop in the gift shops, or sit somewhere and relax with your baby.