puppy and 1.5 year old dog together?

Here is my situation, I have a 4 month old puppy boy and my gf and I are staying at my sister's for a month babysitting her 1.5 year old dog.

And I'm at my wits end with managing and disciplining them both. Especially the puppy. He is constantly play fighting with the older dog (who herself is kind of moppy, because my sister left). I walk them, but the puppy keeps jumping and pulling all the time.

And when I take them out to do their business, they are constantly in each other's spaces that they can't really finish up, so they have accidents inside.

I'm overwhelmed with the whining, and barking, and the ins-and-out of the house all of the time because I don't know if they'll have another accident or not.

Should I just separate them most of the time, or will it fix itself with time?

Thanks