How do you juggle relationship problems with elderly mothers, mother-in-laws, and new problems with daughter-in-laws?

I think it is wonderful when children step up to help an elder member of their family. But I do not think it is a good idea to have the expectation that they will...not every child is suited for caregiving or will want to for various reasons. It is the kind of discussion that should take place sooner than later to avoid any misunderstandings.
One way to avoid disappointment is for all of us to make plans, now, for our future. Look into housing options, buy long term health care insurance, and stop supporting adult children/grandchildren and put those funds into investments and savings. That way, you have a plan for your own elderhood and the kiddos can be those great people who visit and help us out with other things.
The advice you received about giving up your son was harsh and unfair. True, you do need to recognize that he is married and his spouse comes first. But that does not mean that he should neglect the mother/son relationship either. Btw, both daughters AND sons should be expected to show the same amount of attention and respect to family members. In my family, sons are put on a pedestal and are not expected to be caregivers. Then their mothers wonder why they are not attentive to their needs as they age!! hmmmm....
I hope you find ways to find a common ground with all your family members. I find the best way is to have some one-on-one time and share your concerns plainly and without reproach.
Good luck.

I guess that depends on the nature of the conflicts with these women who are important in your life. Is there a common thread? If all 3 tell you that you are too controlling, for example, you could think through ways to lessen that perception (and still do what you gotta do, of course.) If each one thinks the others get more attention from you that she does, or all three think you expect to much of them, or there is any common issue in the relationships, that might give you some clues about where to start. (Even if all three agree, that wouldn't necessarily mean they are right -- it just helps to know what perceptions they have so you can either change what you do or change how they perceive things or some of both.)

I'm not sure I'd count on your son and DIL to care for you in your old age. Maybe. But you might be thinking about what other options are open to you. Also it is good to start planning well in advance financially.

Are you having problems managing your time with these three women? Without knowing the nature of the problem it is hard to give specific advice. But I do definitely wish you the best and send (((hugs))).