Babies can be aggitated when cluster feeding. Could be that he has a wind (my dd has been unsettled the last couple of nights, but with no apparent reason - sometimes they have a wind that won't shift, sometimes something you ate does not agree with them and sometimes you just don't know why they are unsettled). Also, with your MIL hassling you, you will be feeling stressed, and that can stress your baby and make them usettled.
You need to tell your DH that you SERIOUSLY need him to talk to his mum. Get him to tell her that although you (as in "you and DH") appreciate her concern, you have taken professional advice and would like to try bf your way, and would ask her not to comment on your bf. Bf is difficult enough without someone (however well meaning) interfering with the process. If she offers him more formula, he should politely refuse to take it. You really need him on side with you on this one. Take him to bf consultants appointments if necessary, so that he can be educated about aspects of bf that his mum is obviously ignorant about. It is NORMAL for babies to cluster feed, especially when they are so little. It is NORMAL for babies to be unsettled sometimes. This does NOT mean that Gil is not getting enough from you.
If you are still feeling unsure PLEASE ring up La Leche Legue in your area (or a bf consultant or other bf support).
YOU ARE DOING ALL THE RIGHT THINGS and Gil is responding NORMALLY. There have been many threads about cluster feeding = it might help you to take a look at some of the old threads on this topic.
If you want to bf, giving formula is the fastet way to sabbotage your bf efforts, becuase your milk supply will decrease, and you will end up giving more formula. If you want to bf (and you obviously do by your questions) then trust your body and get your MIL to butt out (get your DH to tell her, don't get into a fight with her yourself, as that will just stress you more).
Is Gil gaining weight? Is your HV happy with his progress? Are you happy with the way things are going? These are the important questions - not what your MIL thinks.
Some babies are just unsettled (my first had colic and was unsettled for SIX MONTHS).
Please be aware that giving formula can, in some cases, make babies MORE unsettled. My first's colic only flared up when I introduced formula (something I am desperate to avoid now with baby no2). Also, introducing formula can increase the risks of food allergies (especially if there are any food allergies in either parent's family). I am not anti-formula, nor am I anti women who use formula (I ended up using formula for my ds because I did not get the best bf advice). However, if you want to bf and you can bf then PLEASE do not let others put you off. Get professional assurance if you need to, but remember that your MIL is not a bf expert (her comments clearly show that she is out of touch with current bf advice).