Bloody hell what a stupid owner! You know how pro dog I am SOH but I can think of no good reason why you should be encouraged to allow your DD to approach a dog which is clearly not comfortable with her.
I haven't seen a dog act like this per se. My own Lab doesn't like small children but because of this I'm sensible and don't put them in that position. I'm not saying he'd bite but if a child went toddling/waddling/staggering up as liittle ones do I wouldn't be surprised if he gave a warning growl so I just wouldn't do it in the first place.
The only exception is a pal's youngest. Pal is exceptionally dog savvy, mum to 4 and long term dog owner, LO is very dog aware and mum and I are very vigilant and sensible. LO and dog get on fine but if LO got over-excitable or pushy she would be stopped by mum and taken away from dog. Never a problem and LO is very good and my dog now accepts her as he does pal's older DC.
If your DD were a cat with whom the dog was going to have to live (don't laugh, hear me out!!) I'd be advising gradual exposure with the cat in a carrier and dog on a lead with dog told NO firmly each time he moved towards the cat in anything which was less than a friendly, calm manner. However your DD isn't a cat, you can't contain her like that and thus you can't make progress in the same way. (Works with cats, btw, tried and tested many a time).
I've absolutely no idea why Jinx is acting like this, I hold my hands up to defeat here. Perhaps bad past experience, perhaps fear of the unknown if Jinx has never met a small person. Dunno.
I'm normally TOTALLY against this idea but can only suggest that you insist that the two are kept seperated when you visit. If this were a dog which you or MIL owned I'd say that to seperate would increase anxiety, inquisitiveness and even jealousy in the dog and needed to be worked on (perhaps with a behaviouralist) to restore harmony with a gradual introduction under supervision but dogs are like kids... as much as they can be influenced by early experiences such as the OP's DC who is scared of dogs having been bounded at in the park and thus remember it all long-term, they equally tend to lose track of things when they are not regulary exposed to them.
By this I mean that, for example, the toddler who goes to a CM 5 days a week regularly is less likely to be stressed away from mum than the toddler who goes to the creche once a month. Likewise if Jinx were able to be regularly exposed to your DD every few days and trained to accept her Jinx would get her head around the concept of dealing with a small child, Jinx is IMHO far less likely ro do so when she only sees DD every now and then and training in meeting a 4yo is only sporadic and interdispersed with her regular life.
I rarely advocate seperating a child and a dog but I can't see any other solution given that DDs contact with her is infrequent and that you have no control over the training of Jinx nor can you offer consistancy in giving her contact with young DC.
BUT.... I'm not a behaviouralist and I'm useless with children (see mine for proof!). All I can say is that if only for dog-centric, acadmic purposes I'd be interested to know Jinx's past and whether she was reared with her owner's DC or came to them in later years. Perhaps my best advice is that you repost in the Doghouse for the attention of minimu who is a trainer/behaviouralist as I'm sure she will have the answers and rubbish all I've said because she knows far more about dogs than I do, I just save 'em!