Prince Hygiene (SS at the time age 6) would run up between me and GG and physically try to separate us when out at the hardware store, etc.

He would cling to GG, follow him into the bathroom, plop himself between me and GG on the sofa, etc. etc.

She's "marking her territory"
Hopefully DH doesn't secretly think this is "cute" or amusing" or "oddly flattering" b/c a child can pick up on that even if he isn't outwardly displaying it.

And yes, if I had to call it, I'd say she will be jealous toward your baby. We've had posters tell us about skids as young as 3 actually expressing their desire to cause physical harm to the SM's new baby. I'd keep my eye on her.

Don't let her get the desired reaction. Act like it means nothing and ignore it and keep being affectionate to DH. This jealousy is annoying, but misplaced. DH needs to make sure he doesn't play into it as it can be like a drug to some fathers. Most young kids get threatened when a new baby comes along. You can be reassuring and give her some one on one special time. Kids are not spouses and parents who give them that status by placing them above their significant other are idiots setting up doomed relationships for everyone. Also if BM is in the picture they usually make skids feel insecure about their importance to their father when a new woman is in the picture out of spite. Hopefully because she is only 3 and DH is not playing up to these antics, she will get over it with a little encouragement from you both that you care.

I agree. If she, for example, plops down in the middle of you and DH say on the sofa, get her a bean bag chair that she can sit in and then have her sit there.

Calmly explain it's rude to plop down and squeeze in the middle of two people sitting together, then move her to another area.

Don't let her see you get angry about it. Just keep responding firmly and calmly.

If you notice so much as a "grin" from DH when she does this, that has to be addressed.

My SD3 has never said anything like that to me but she does definitely get jealous at times when my fiance is showing me attention/affection. For instance, we could be cuddling on the couch and she'll come over every 5 minutes, "Daddy?" "Yes?" he replies. "I love you," she says. "I love you too," he replies. This exchange happens about 20 times every evening and she especially likes to do it when we are talking so she can interrupt. She also will come in and ask for a hug frequently if we are cuddling or she'll just come up and sit next to him on the couch and start talking during our show/movie just to get his attention. It used to bother me, especially the few times she actually tried to take over his lap when I was already resting my legs on his. However, I realized that if I didn't show that it bothered me, she eventually gets bored of doing it. Jealousy only works if someone else will play along with it. Since she can tell it doesn't affect me to share her father and that I am not jealous, she seems to feel less threatened by my presence and this game begins to get old faster.

Many children do that. When DH and I first got together, SD was 3 at the time. Any affection between us made her super uncomforable. She would try to sit in between us, take his hand, and even sometimes try to make him get up and away from me. It worked for awhile and then DH realised WTF was going on and he put a stop to it. He ignored all of her attempts. Eventually, SD got used to me being around and she doesn't remember a time that I wasn't around.

I did it to my mom and step dad too. I felt like he was "stealing my mom" and I was 3 at the time, and I had no idea how to handle those feelings. Most children that age have no idea why they are feeling what they're feeling (jealousy) and they have no idea how to handle those feelings so do what they know how to do; They stop you two from doing the thing that gives them those feelings.

Your DH needs to put a stop to it. I'm sure she will eventaully grow out of it, but only if your DH stops it now.