She is still very young to know how to keep a command so do not expect that at this time. I would not expect a puppy to keep a command until nearly a year in an environment that is interesting to it. Company would be interesting to a puppy. Expecting the dog to stay in a sit for any length of time is reaching for a miracle. Even my service dogs cannot do that and they are trained daily.
When you want her to stop jumping , give the off command m providing she knows that and have handy something handy that will keep her busy enough to then respect the off. I find that pups that are bored are most in trouble. Provide the puppy with mind stimulating toys such as puzzles , Kongs, treat dispensing balls so the dog has to use its mind. When they use the mind they tire easier. Also once the dog is off of you and you give it a frozen kong stuffed with yogurt it will keep them occupied and it will be the reward for getting off of you. So, Fido =Off= down- Kong. this way you are telling the dog many things, you want the dog to off of you, then to down and for doing the down instead of jumping there is a reward at the end.
Most of the puzzles and treat dispensing balls can be filled with the dogs daily kibble so they are constantly learning to work for their food, then they are likely to work for you when asked.
As humans we tell the dogs what we don't want them to do but rarely back it up with something they can do instead that is just as interesting and will earn them a reward.
You did not mention what type of training you do at pet smart but I would do clicker training at home and I would train several times a day in short sessions. Dogs do not carry over what they learn in one place to the next place so she needs to be taught everyplace you intend on taking her.
Also get a good leave it command in place so when you see she is about to do something or get something you don't want her to you give that command and she should stop in her tracks and put her attention back onto you.
At this point for your mom's safety you may want to set the dog up
in an area she cannot get to your mom and knock her over.