Dog troubles (long) – I don’t know what to do.😕

So we didn’t have a dog until my daughter was 6 months old. So we’ve had her for 2.5 months now. We took her in because she had nowhere else to go and we didn’t want her to end up on the streets or go to the pound. Well she’s about 6 years old so on the older side. She’s a pitbull/german shepherd mix I’m pretty certain. But the thing is, is that she doesn’t listen and I’m a SAHM so I pretty much care for her and my daughter full time all week. It gets hard because I don’t think she was ever trained and we try to train her, but it’s pretty much been a lost cause because she’s older and has already set her ways I think. She barks nonstop (normal dog stuff, no biggie), gets into the trash so we have to keep the cans up, doesn’t listen to me at all and I’m very stern with her, she tore up her dog bed, breaks out of her cage every time we leave and potties all over the house, I had gotten in the shower once and she had pooped all over my daughter’s floor🙄, and we’ve just had lots of trouble with her from the start. There’s more issues, but that’s just some. The barking is constant though and she wakes my daughter from sleeping every time. I love dogs and am very patient, but it gets so hard to look after her and my daughter at the same time. I have to put a leash on her to go outside because she will run off, bark or try to attack other animals or people, and if I leash her to the tree she can break it off. Plus it’s just a rule to keep the dogs on the leash/chain where I live. She is very jealous too, not an aggressive jealous, but she will get in the way if people are talking or not paying attention to her. She’ll shove into people and get in their face and we have to constantly be on her if we have people over or put her in another room even though I know that won’t help, it’ll just make her upset. She gets in the way if we are holding my daughter and playing with her and we’ve really been trying to correct this behavior because I know it isn’t good. She’s never bit her or got aggressive with her or got aggressively jealous. But the jealousy is a bit much. There have been times where I am laying with my daughter or have her on the couch changing her and the dog has jumped up or ran over to where I am and almost trampled my daughter all because I’m talking or singing to my daughter. She has gotten jealous and mad to where she’d go potty on our things. I’m just at my wits end. I don’t know how to correct her behaviors or try to get her to listen to me. She will stare and just wag her tail if we’re trying to get her to listen, or she’ll just continue what she is doing. We don’t hit her or anything so I don’t tolerate that and won’t. She does have a cage that we’ve had to zip tie around the edges to keep her from escaping or breaking it when we are out of the house.🤦🏼‍♀️ we only use the cage when we aren’t home. We’ve asked around if anyone around us that we know could take her in but either no one has the time, the room, or they just can’t have a dog. I would hate to re-home her, but I get so stressed out everyday and about have 50 million breakdowns. My daughter is teething, been very clingy, and hitting the 8 month sleep regression I think, so it’s super rough. I don’t know what to do. Does anyone have any training tips or how to get her to change? I feel like I need a dog whisperer lol. We do reward and praise her when she has good behavior. I don’t really want to re-home her, but I’m just trying to figure out things that can help correct her behavior. I’m a very stressed, exhausted person right now!!