I feel so, so sorry for both the daughter and the mom.
Clearly something is wrong here.
It sounds as if maybe either the mom, herself, was a victim of something at some point in her own life and is therefore wildly overprotective of her daughter. Or the girl has had trouble at some play date and told mom, who interpreted as the girl being threatened and who now hovers fearfully. Or possibly the mom has an ex who was abusive and stalkerish, and whom the mom fears can get at the child if mom so much as leaves her for five minutes outside the security of school. Or --the mom may simply be very lonely and awkward, and not good at making friends, so she hangs on when her daughter goes on play dates, in order to get some adult-mom company.
In other words -- you can't know what is making this mom so very, and so pathetically, overprotective. She also seems to lack the "social brakes" that most of us develop and which help us recognize when it's time to go home--those inner intutions that tell us when we're on the verge of overstaying our welcome. Some people do reach adulthood without those brakes ever developing, and they often don't read other people's social signals well (such as not "getting it" when a host parent says, "Well, we really need to get our dinner going soon...." as a cue to leave, etc.)
And buying your child clothing without your permission -- yep, that really was stepping over the line. I assume you had a strong talk with your child about accepting the dress, and I hope you returned it--? And told the mom that you had said no to your child and had returned the dress?
As someone already posted, you could frankly ask the mom, "Is there something wrong with Jenny?" Though....I might phrase it more gently as "Is there something going on with Jenny that makes you prefer to stay through play dates? Because I note that you do prefer to stay, and though you said you just don't trust leaving her, I wonder what I can do to put you at ease enough that the girls can have their time alone together and you can get some well-deserved free time for yourself."
Or alternatively, only meet this mom and daughter at the park or on other outings when you are free and willing to hang around yourself.
It seems a real pity for Jenny to suffer and go without play dates just because her mom is either socially clueless (which may not be mom's fault) or because mom has had some past incident that makes her irrationally protective. It would be a real kindness to the child to continue to have play dates if you can get them more on your terms.
Has the mom actually just sat in the house while you worked and the kids played? If that only happened a time or two, letting it happen every single time might get the message through to her: "I really do have to work and I am just a few feet from the girls. It's OK if you want to stay during the play date, but I'll be working, and if you wanted to go out and get your errands done and pick Jenny up at 5:00 that would be great."
You ARE giving her specific ending times on play dates so far, aren't you? It sounds as if they are rather open-ended if she and Jenny are still in the house at toddler bedtime. Be assertive with farewells and be sure to say "The girls can play until 4:00 but at 4 we need to get Child ready for dance class" or "we will be leaving just after you leave at 4 to go to X," or whatever. It sounds as if this woman might need very specific time frames and then you might need to, with your daughter, walk to the door and hold it open with a big smile and say, "I'm so glad the girls had a good time but we've got to say our farewells and get Child and Toddler ready for X now."
I think it's clear, though, not to let your daughter go anywhere alone with this mom and Jenny, after the mall incident.