Jackie throughout the series (leading up to DD)
Jackie tries to hold Rose back because she is afraid of losing her daughter.
She has seen what happens when you reach for the impossible (scattered sketches of failed inventions, no money in a council estate, a head so full of dreams that you miss the car coming down the street). So she tries to hold Rose back, at least some attempt at keeping her grounded. She's not sure she's strong enough to hold Rose together once everything crumbles when she is patched so precariously herself.
It's why she was so adamantly against Jimmy Stone (though her dislike of the boy has been justified) and her reasons for disliking Rose's job at Henrick's (airs and graces and reaching for the stars). She thinks she's managed reasonably well, Rose has a steady job, steady, safe boyfriend. Until Rose disappears for a year and comes back with an honest to God alien and blows up Downing Street to save the world; she wonders where she went wrong.
She asks him to promise that Rose will be safe, can see him struggling with a response. He gives her the truth and she grudgingly respects him for that. Notices how desperately he wants to promise that her daughter will be safe. He watches her daughter, friendship and love, and devotion, and need in that blue gaze. The Doctor wants her daughter safe, but he needs her with him, and he will do everything in his power to make sure he can have both. Jackie accepts his offer; it's the best she's going to get.
The Doctor sends Rose back. That simmering jealousy and dislike that Jackie feels towards the man who stole her daughter fades. He sent her back. They all know what this means. Jackie knows the only reason he would send Rose away was if there was no way she would survive (and she is quite certain from the spaceship sitting outside and her daughter's wild eyes that he wont survive this either). So when Rose begs her to understand, desperately tries to get back, because she love's him enough to die with him, Jackie calls in a favor, brings in a truck and sends her daughter back.
It's Christmas and the Doctor's crashed the TARDIS, changed his face and fainted. Jackie watches her daughter, who seems slightly wary of this new man, but still just as desperate to save him. She's not so certain she believes Rose's claim that this new pretty man is the same as the old soldier. It's not until they are attacked by a plastic tree and Rose pleads with the Doctor for help, that Jackie believes. There is no way she can doubt him anymore. Even catatonic, the Doctor is obvious in his love for her daughter. When he asks Rose to come along, stumbling over his words in his haste to make her understand, Jackie knows she will never get her daughter back for good. She resigns herself to infrequent visits and odd trinkets from places she can't pronounce. But she does force them to stay for Christmas dinner. This man seems more accepting of domestic, and they stay a week, with promises to visit more often when they leave.
Rose calls her after the Doctor disappears to 18th century France, leaving her and Mickey alone on a spaceship centuries in their future. Despite Rose's fears that the Doctor might get bored of her and abandon her in Aberdeen (Jackie is not quite sure why Aberdeen is so terrifying), Jackie knows the Doctor will never willingly leave Rose. He might send her home if there is something particularly life threatening, but never for good. He will come back (no matter how many of the face changing regenerator-things he has to go through). Rose may have waited five and a half hours for him, but Jackie knows he would have waited however many centuries necessary to make it back to her. She also knows he'll never tell her daughter that.
Oh, he has Rose's faith and love and devotion, he believes in her and loves her back, but he will never tell her. Jackie is glad he loves Rose (though why can't that damned man say it!), but it worries her as well because she knows he'll never let Rose go and she wonders just what he will do (how far he will go) when he comes face to face with her daughter's mortality.
He is starting to believe in the promise of forever, expects it almost, Jackie can tell. If they were both human, she imagines they would already be married (wonders if they are already married by some strange alien custom and just have not told her). They are both reaching for the impossible and Jackie hopes for them both that it is achievable. This new Doctor is more comfortable with himself, her daughter is more confident. But when does confidence become hubris? She sees it in them both. The belief that they can do anything as long as they are together. She doesn't want to tear down those beliefs, because their teamwork keeps her daughter alive, and such devotion and trust is a beautiful thing to witness. But she also wants to shake them. Force them to see how dangerous it is to ignore the things around them, to believe themselves safe, invincible. The Doctor cannot solve everything, even if he thinks he can. Rose cannot be with him forever, no matter how hard she tries.
Every time they come back, she loses her daughter a bit more to the overpowering draw of the Doctor. She fears that one day, her daughter won't come back at all.