Hi, your observation is correct. It appears , the makers have rushed in to introducing Mukku without any strategy or they may open up more of her in the coming episodes.
In my opinion, Mukku is not weak or childish . As per story so far, she was a victim of DV, not in touch with Brother who is her only family member for 10 years, travelled across world as a single, unpredictable , weird behaviour, I think her DV is strongly burried inside which flare up on any small instigation. The fact that she chose Vanraj as partner, went to Shah house to stay looks like she is aware of what she is doing only to assess in person these people who abused Anu. Though the reason she gave for going out is the comparrison of Cake, she never directly or indirectly said or did anything to hurt Anu. so it may be with an intention to bring Anu / Anuj closer .
The fact that she travelled alone for 10 years, would have made stronger and smarter except the deep wound. Probably she is testing Vanraj , which is possible only if huge amout is shown to him. ( carrot to horse)
She is also not jealous of other couple , she praised almost all couple in shah family and very sincerely and openly want Anu / Anuj marriage. She also wants Vanraj to accept Kavya and give her a chance. May be all these are to really make Vanraj forget Anupama and stop stalking her. So she herself can settle down in a family environment and later may be move on if she gets a good partner.