I really feel for you because of the time it took you to care for your mom and deal with her estate. I have been there. For you, it puts a hole in your work history -- but it is a hole you do not have to leave as just a black hole. I agree with you that the other two short jobs need to be on the resume or it appears you didn't work at all since, what, 2011 or so? But you also should mention (though not put on your resume, naturally) that there are gaps in your work history due to stopping employment to care for your terminally ill mother and to handle her estate.
You can offer that if you choose. "I know my resume shows some gaps in recent years and I would like to explain those. I took time off working to care for my terminally ill parent, and also time off to deal with her estate. While I realize those are personal issues, I also want you to understand why there were some periods when I was not in continuous employment." You do not HAVE to offer this, by the way, but some employers--I would think any decent employer--would probably be impressed by your frankly addressing gaps before they ask about them, and would be impressed that you took on what amounts to a full-time job of caring for someone else.
Be aware that employers who are, to be honest, nitwits will possibly then ask, "Well, is anyone else in your family going to need care that you'll want to take time off for?" That would not be a legal question, just as it is not legal to ask about your marital status or whether you're pregnant or have kids or your sexual orientation etc. (The one interview in the past where you were asked if you were married? That interviewer was just plain stupid--that can't be asked. Jerk.).
You don't want to work for anyone who asks whether you have other ill family members and would leave to care for them. You possibly DO want to work for the interviewer who says, "I understand about taking time off to deal with medical and estate issues."
Remember, you do not have to provide a reference for every single job, no matter what resume books tell you. Provide them for those jobs that provided your "many years' experience in retail and call center jobs."
As for that outside sales job, you still have to list that too even though you don't know where they went--and can't you locate someone, anyone, from that job via LinkedIn, Facebook, just plain online searching? If the whole firm is out of business, well, that does happen and it's not your fault, but you will appear more in touch if you do put it on the resume and say it's gone out of business. If the firm exists but that branch is gone, the larger firm can still confirm your dates of employment and title--which is all that many references will do anyway. Many references will no longer give opinions on the person at all, out of fear of being sued, but will only say "I can confirm that R. worked at our office in XYZ from December XX to June YY in the position of Whatever."
That too might help with the two terrible jobs. If they are large chains they are not very likely to give you a poor reference because they won't really remember you after short stints -- they can confirm you worked there and that's likely all they'll be willing to do. Especially for lower-level sales or call center jobs, unless an employee totally tanked, or washed out due to drugs or drink etc., employers are not going to take time to provide much of a reference for good or for ill.
Like someone below I wonder why you don't mention temping--? That can help build a resume. If you have done call center work you can parlay that into saying you have skills in time management (juggling lots of calls), setting priorities and much more. Search online for tips on how to turn call center and retail experience into skills lists for a resume for temping. I've known people who were very happy temping and others who used temping to test out workplaces and found permanent jobs when the employers liked them enough to make them staff.