First, and most important, the adults have to be on the same page, so to speak, and they are not. This should be discussed among you. Second, the symptoms you describe at school are consistent with a Hyperactive-Impulsive (not Inattentive) type ADHD. This is a neurological condition and may invite pharmacological treatment. Third, to manage the behavior at home, you and his father should read Lynn Clark's SOS Help for Children and follow the guidelines.
First of all, I highly recommend reading a book called: "Scattered: How Attention Deficit Disorder Originates And What You Can Do About It" by Dr. Gabor Mate, M.D. It was a real eye-opener to me - I did NOT want to put my son on medication if at all possible - it was going to be the very last resort. My son had behavior problems - but through persistence and a lot of hard work, by 4th grade he was fine. He was kicked out of a private school in 1st grade for hitting the teacher in the face. Then in public school I was always being called for “conferences” with teachers and/or principals – for not doing as he was told, being "too fidgety" and never sitting or standing still, not "cooperating" in class, and also “suspended” for hitting/pushing other kids (he knocked one boy on the ground, and the boy hit his head on the ground and had to be watched for a head injury), etc. Then there were the struggles at home - getting homework done was a nightmare - I would sit for 3 hours with him, working on a worksheet that should have taken 20 minutes .. constantly re-directing his attention, or when he stubbornly refused to do the work, I told him we were going to sit there until it's done, even if it takes all night ... (and yes, I worked full-time, so it was very difficult for me - I had another child, and a child for a husband - who was alcoholic, so I had to deal with him and his absences until I wised up and divorced him - my son had a "reason" in my eyes for his behavior - our house was chaotic quite often, his dad coming and going, etc. But I was a very stable presence for him, as were his grandparents - and yes, the grandparents MUST know what your "rules" are, and follow them - if they won't, then it's simple - they don't take care of your son - I know that's harsh, but their not "joining forces with you" is RUINING him. You are all going to be so sorry when he's older, if you don't stop your wishy-washy parenting).
Kids will try to TEST you on EVERYTHING - your patience, your rules, etc. - You MUST OUTLAST your child whenever he turns something into a battle of the wills - Kids are SMART - they know adults are tired and will "give up" sooner or later - If you love your son, you will dig your heels in and not quit - no matter how tired and battle-weary you are. Kids are master manipulators - they will pull and tug on the "heart strings" of anyone who is sappy enough to fall for it. Sure, we love our kids and want to smother them with love - and you SHOULD do that - but you must also SET BOUNDARIES. And I'm not saying to be "authoritarian" or "harsh" - be FAIR and JUST. ALWAYS tell your child what the consequences of his behavior will be, when you are "making the rules" - don't make him a victim of your lack of communication – we have to be able to clearly see where that line is, that we can’t cross, so that we can’t claim “ignorance.” This also teaches them “responsibility” for their actions - that they can't blame anyone else for their choices. Tell the grandparents that if they never let your son "suffer the consequences" of his bad behavior or wrong choices now, while he's young, it's going to be 100 times harder on him later.
Believe me - I also used to work in a juvenile jail - I saw the effects of "bad” and/or “emotionally or physically-absent” parenting, every single day. If you don't discipline your son (teach him how to follow rules, to be subordinate to appropriate authority, teach him he has to do things simply to learn "responsibility," etc. - all while you're loving him unconditionally), you will be doing him a great disservice. You need to balance love with discipline to create self-esteem - so that a child will feel wanted and like he belongs in the family unit (validation) - that he plays an integral role and has something valueable to contribute to the family unit (and that isn't always something that's "fun and/or exciting") ... Also take a look at your "environment" - if the "stress," "anxiety," "unhappiness," or anything like that is evident to all who live there, that will affect your child's behavior. Take it from me - marital problems DO affect your child's behavior - because your "problems" or "anxiety" or "stress" or "unhappiness" is something he knows he can't control. A child has an extremely hard time functioning in any kind of chaos - whether it be emotional, physical, financial, etc.
Also, spending TIME with him - teaching him HOW to get things done (organize his time, thoughts, etc.) will help. I figured out at some point that my son was not like my daughter, as far as "organizational" skills were concerned ... he simply did not know "how" to begin to organize, keep track, etc. Sometimes we as parents miss the "clues" - we think our kids automatically know everything we do. Some kids simply need more direct guidance and detailed instructions and "help" in learning how to "survive" in all areas of life. My daughter was an avid listener - she listened to everything everyone said - she was able to "pick things up on her own," and her constructive reasoning was more advanced than my son's. And I learned that sometimes he did need to be "reminded" over and over and over again ... no matter how exasperating it is - be CONSISTENT in your parenting - and make it known to others that you expect them to respect your wishes and your rules when it comes to your child, and that if they can't or won't, that you won't let your child be with them as much anymore - because their lack of respect for your authority and your rules is what the child can see - and if he sees others disrespecting you and/or devaluing you as a parent, he's going to try it, too. I know it doesn't seem nice to tell grandparents stuff like that, but you must make them realize the detriment their lack of "backing you up" is causing to your child. Don't do everything based on "feelings and emotions" - because they're not reliable all the time.
Feelings change and come and go and ebb and flow ... no one can predict what a parent will think today vs. tomorrow - and when kids "aren't sure" what's going to happen next time, it makes them confused - and of course that's going to possibly cause bad behavior. How would you feel if your boss "changed the rules" and what you can and can't do, or how things should get done, from day to day, based on how he or she was "feeling" that day?? Wouldn't that cause you to "not react well"?? But "having rules and guidelines" and "knowing the boundaries" impart stability and give us the freedom to choose - to learn how to "work within the boundaries in an acceptable manner."
I kept with it, and as 4th grade came, the "behavior" problems suddenly stopped. Of course, I did a lot of praying during that time .. so I credit God (and a miracle!) as much as my own efforts. Throughout the rest of his school years, teachers always complimented me on how polite, respectful and well-behaved my son was! Despite his lack of a real father (who died when he was 15, but he always had my brother and my dad - family support is WONDERFUL - if they want the same success for your son as you do and therefore SUPPORT you in your efforts) - my son beat the odds of being diagnosed with ADHD, without medication. YOU CAN DO IT. And basically, you have no other choice, if you really love your child.
Medication should be your absolute last resort - when you can, with all honesty and good conscience, say that you know you've done all that was humanly possible within your powers, without it. I will never tell anyone to never use medication - because I know that sometimes it's absolutely necessary. I just think that too many people are too quick to use "pills" to solve behavior problems - when in fact, many "behavioral" issues are due to a lack of boundaries (or lack of "knowledge" of what, exactly, those "boundaries" are). And that's another good book - "Boundaries" by Drs Henry Cloud and John Townsend.