When my kids were of different ages, their grandparents would take them one at a time. Sometimes my mother-in-law wanted to have time with the baby. Sometimes my mother-in-law wanted to hang out with the toddler. And sometimes my mother-in-law, just wanted the older kid. 
 

As a grandma, you have a right to say you just wanna hang out with the three-year-old. And I think it's OK to tell the 13 year olds mom that she doesn't seem to be having too much fun with you.

BM will cut you of their lives if she feels like it. I've been there, and there isn't anything you can do about it.

I hear so much frustration from everyone, including myself. In the end, the SK has the say if you see SGK's. It does sound like you are trying to be so fair, and have a lot of "patience". The child does sound like there has been a lot of trauma in her life. You are being fair, and don't feel guilty about spending time alone with your bio grands.

Honestly.. I don't think it's unusual at all for grandparents to see even all their bio grandkids at different times.. intervals..etc.. depending on proximity.. closeness in relationship.. ages.. just all sorts of factors.

So.. absolutely.. you can and should personally spend as much time as you want (and their parents are ok with..lol). with your bio grandchildren.  Your HUSBAND can choose to spend time with HIS bio grandchild that is older if HE wants to.. and you would be kind to host her yourself.. and not be totally exclusionary.. but no guilt to make things absolutely equal with her.. you can't make up for the fact that she has failures for parents.. (or had).. it's sad.. but not your making.. and not really something you will be in control of fixing.. 

Nope, it's not unfair to want to spend time only with your bio grandkids. Teenagers (especially ones that aren't related to you) can be unpleasant to be around, and doing things with kids of very different ages can be difficult. But if your DIL is the type that will restrict your access to your grandchildren if you don't take both kids, and your son won't/can't overrule that, you may have to play by her rules.  

different ages, different interests, different visits. do the 14 yr old's first, take her to a movie and lunch. then the 3yr old's visit alone and if the 14 yr old complains remind her and her mom firmly that she had her private visit, this time wasn't for her so she will not be going too.

You want to be fair but it isn't fair... to your GD. There is no way to blend a visit with a teen and a toddler. She doesn't get to invite herself.  Doesn't she have any bio grands at all?

I understand your desire to make her happy but she clearly doesn't want to be happy, she wants to be miserable and make everyone else miserable. This isn't uncommon with teens.

Tell her mother that she has outgrown you and that she needs to find another solution for her daughter because she hates being with you. She is not your responsibility. Her mother sees you as a babysitter who takes her daughter off her hands for a while.

Not your monkey.... 

Give your bio grands the love and attention they deserve and that you want to give.

As for your GSkid's behavior, do not tolerate it. When she is with you, she behaves. Period dot.  When you have both the BGK and the GSkid, keep the GSkid controlled so they can have some interface, but you can have some discussion time iwth your BGK.

When GSkid whines and manipulates. Put her ass in an isolated corner to hold the walls together with her nose until she gains clarity that she has no choice but to adhere to the behavioral and performance standards YOU require when kids are in your presence.

If your BGK misbehaves, the same standards and consequences should apply.

IMHO of course.

 Not sure  if you live close, but why not take the little one during school hours. You could make a weekly thing. Then older kid can't come.