We recently purchased a "Decker" Rat Terrier.
If you aren't familiar with "Deckers" they are Rat Terriers that have been bred for size and hunting and weigh around 25 - 35 lbs. mature.  Some males can reach 40 lbs.

I'm a long time dog lover/owner and I've had dogs all my life but I've never had a Rat Terrier before.
I know how to do obedience train but this newbie is challenging.

QUESTION 1:
Anyway our puppy bitch "Shelby" (around 2-1/2 mos.) is very smart but also VERY exuberant and persecutes our 2 older and smaller Chihuahuas (9 & 11 years old) by wanting to play too rough with them or uses them for chew toys. The younger male Chi is willing play with her but then becomes overwhelmed with her size and tenacity.  Our Chi bitch wants nothing to do with playing with the new comer and will try to ward her off with bark/snap warnings but Sheby doesn't always heed the warning and will keep at her.  I've been trying to teach her not to do those things by telling her NO! and a correction jerk on the collar  and giving her a toy to play with or play with her but I cannot spend my whole day playing with her. I have even resorted to smacking her on the butt when she doesn't respond to the collar jerk.  That only works short term and I don't want to make a habit of hitting her. She has plenty of chew toys but the minute I turn my back on her shes back at tormenting the Chi's.  I don't want to break her spirit but on the other hand I don't want to allow her run rough-shod over the 2 smaller dogs especially since our older Chi has Congestive Heart Failure.   There seems to be no wearing her out with long walks or human attention, etc.  We have a huge fenced in backyard but if I put her out without the other dogs she mainly just stands at the door barking to get in.

QUESTION 2:
On the days I work ( 2 x weekly) I put her in her crate and shes trashes it and goes potty all over her bedding.  Shes rips up the newspaper and dumps her bowls over.  She has toys and chew toys in her crate to play with.   Half the crate is bedding and half newspaper.  I know she can hold herself because she often goes all night without going in her kennel.  I think shes just upset because I'm gone.  Even kenneling the Chi's right next to her doesn't seem to help.

Thanks in advance  for any  recommendations on how to handle this dynamo.

Welcome to the site. I am sure our training moderator will have some ideas for you regarding the roughhousing with the Chi's. As for the crate, to me it sounds like it is way too big for her which is allowing her to potty and destroy it. It should only be big enough for her to lay down and turn around. One blanket for now will make it easier to clean up. But if she has enough room to potty and then lie at the other end, she will. You could get a divider for the crate to make it smaller until she grows. Kongs also can keep then busy in there while you are gone. A 2 1/2 month old puppy is a handful, but she will grow out of it with time and consistency on your part.

I would not leave bowls in the crate... I would be sure the crate is big enough for her, but not too big. She's just a pup, so shouldn't be in the crate for more than three hours at a time, so I'm hoping she's not in the crate on the days you work for a long period of time. All day (8 hours) is too long for a 2-1/2 month old pup.

Puppies often pester adult dogs unmercifully. Well-socialized adult dogs with good temperaments may set limits with puppies with a growl or snarl/snap. This is normal and should be allowed. Your puppy shouldn’t be left unsupervised with either or both of your adult dogs until you’re confident the puppy (or the adults) isn’t in any danger. Your pup (because of her size and energy) could very well unintentionally hurt your older two dogs. During the times you cannot supervise them, put the pup in his crate thereby eliminating the possibility of him hurting the two older dogs. When they are all out and the pup becomes too playful with the two smaller dogs, watch them closely. You can tell when things are getting out of hand... you can either correct the pup by squirting her in the face with a water bottle or put some coins in a can and shake it to get her attention. Call her to you, and give her a treat... rewarding her for (1) listening and (2) coming to you.

Some of this will work itself out in time as the pup matures, but certainly at this point I can see your dilemma and the need to protect your older dogs.

You said you have the crates next to each other. How close?? If I were only a couple metal bars away from someone I wanted to torment, it would definitely antagonize me and make me want to go after them as soon as I got free. If you can, try putting the crate in another room, or in a spot where they can't see each other during the day.

EDIT: Remember, the crate is supposed to be a safe and happy place.