DD will be 2 in a few days and we are definitely in the middle of a "mama hold you" phase. I think she's just in a space where she's feeling the need for some additional connection to DH and I.
Does your DD run/play when you get to a destination where you're no longer into linear travel--like does she run/play in the park, at a baseball field, near a park fountain, in the woods, stuff like that? My DD is not that interested in walking in a straight line at a mama-directed pace--but once she's free to go where she likes, she's all over the place. So I try to make sure she gets some time everyday in a space like that, or just in the backyard. As much free rein as I can give her (stay off the roads, stay within general eyesight).
Will your DD walk if you go "for a walk" at her speed/her direction? DD likes to determine the speed and direction of our "walks" sometimes and when she's allowed to lead, she does enjoy walking on her own.
If you're worried about exercise, can you find some ways to help her get exercise while still feeling close/connected to you? Like maybe some Mama-led jumping/stretching/touch-your-toes/dancing sort of thing in a park or backyard? Would she be into some kind of toddler gym activity?
The rest of the time, I just wear her in the Ergo, wrap, or ring sling. Or push her in the stroller, if she'll allow it.