Our informal rule is that nobody else (grandparents, teachers, etc) is allowed to give out-and-out sweets (cake, ice cream, candy) until our kid is old enough to PROPERLY brush and floss his own teeth (he is currently a bit over 2). For some reason I find that phrasing it to my parents as a concern about dental hygiene plays better than a concern about other health concerns. I guess perhaps because there is some sort of end to that (at some point my kid will learn proper dental hygiene), it's not just an open-ended decree of no sugar ever. Also, out dentist is MUCH more aggressive about discouraging sugar and harping on the evils of various foods with regards to potential for tooth decay than our pediatrician is about doling out diet advice. So I can VERY honestly say that our dentist read us the riot act about what foods are not okay for a toddler and my parents will be nodding along in agreement and saying oh, yes, you should listen to your dentist. Whereas when I tried to tell them I don't want my son to be a sugar addict they started coming back with "oh, it's a little, it won't hurt, you didn't have much sugar but you have to have some fun, blah blah blah". My parents also only see us 1-2x/year so I will admit it is not a huge concern, they simply won't have much power to control my child's diet.
That said, our daycare serves lunch and snacks and while they adhere to some very strict nutritional guidelines about added sugar, their food is NOT 100% sugar free. The kids definitely occasionally get Hawaiian rolls with their lunch, for example, and while they have assured me they do not use juice as a sweetener, I could believe that some of the baked goods contain very concentrated applesauce. So I would be lying if I said my kid has no sugar.
We do not serve sugary foods at home and generally fruit is served as dessert rather than as part of the main course, so he has to make a decent attempt at the protein and veggies before he gets fruit. We don't keep juice or jam in the house (I do make things like applesauce and fruit compote, though we do not offer them daily). My husband and I both feel pretty strongly about keeping his diet low in sugar so we very rarely/never buy things like kids crackers, fruit pouches, etc. Once you start reading labels it's really pretty shocking how junky many "healthy" or "wholesome" kids snacks are.
If we are at a party, I do not forbid the sweets but again, I try to make sure my kid eats some healthy stuff first. If we are going to a party I usually pack healthy/low-sugar snacks and so far I have had reasonable luck at getting something like some peas or cucumber slices and a string cheese into him before he spots the other food, and if he has something in him already he is generally less interested in the snacks. We have been lucky that so far he has had limited interest in the junky stuff--he has yet to request a juice box, for example. Last week his daycare had a potluck and someone brought mini-cupcakes, he was agitating for one so I gave him one with most of the icing scraped off (the icing being the major source of sugar, IMO). He tried a bit and then decided he wasn't interested.
With regards to your MIL, I think you do have the right to veto sugar completely or set down rules as to when it's okay. And it is also fine to flat out tell her that sugar does not "give energy" (okay, it gives you a temporary high...and then a crash) and that she needs to back off. Personally, I am not okay with sugar being a regular part of our M-F routine. At a birthday party or special holiday, fine---I recognize that in the long-term I will have limited control over that. But for it to be something they have daily...just NO. I have struggled a LOT with sugar consumption and I am sure the fact that my childhood home was always stocked with cookies, ice cream, and chocolates contributed.