I'm Irish for context, the wake is held for roughly 2 days at home before the funeral so family and friends are welcome to come and share their stories of the person and celebrate their life
I was taken to funerals even as a babe in arms, and my aunt was sexton of the local chapel and so even as a young child (say 3 or 4 upward) she had me helping her get ready for funerals. The coffin coming in, people being sad sometimes crying, getting the church already setting out things, arranging flowers and then fading into the background.. (i called it like hide and seek while still visible),
Before my DMs death, esp the 3 youngest grandchildren - the others were adults and could visit her in hospital at any point without the organisation 3 young children took as we knew it was an emotive visit and make sure had somebody out in hallway who could take any child for a walk if upset and help comfort them. We were lucky in one-way cos of the situation we were in, we had open-ended visiting times,
Which while tiring for her they helped her rally when no hope was in sight
In this case, going to their requiem mass and then to final resting place. (Wednesday evening around 8 pm and mass and burial at 11 am on Friday), friends sat up the 1st night and family the last night usually followed by a family and friends meal afterwards.
They were prepared that each visit they had, could be the last time they saw Granny X as she was very sick and in pain and was going to live in heaven and look over them and help them do good things and have no pain. She would miss all of us. At that point, they were 8, 4 and 18 months. That fluffy version helped them cope with other losses later on in their lives.
They attended the wake, overnighting in a friends house so it was easy, The youngest 3 passed around plates of sandwiches and biscuits and were generally fussed over.
A friend of mine who was a children's nurse who now works as a nurse trainer was impressed at how 18m was handling it, as people entered the room where DMS body he was over to grab their hands and take them to bedside (about 2 meters away) with the explanation of Granny (her name) has gone to be an angel, she is watching you, lets look at the ceiling and wave. He also kept hopping up on the bed so could see into the coffin and looking at a photo and then at his Granny, working out AWAY and HERE. Away - was how she was referred to for quite a while.
The approach worked for us as children can think of all sorts of things in their heads which are far worse than any reality.
Another example from my life, my dad died when I was between 5-10 years old. (being vague for MN) I knew he was sick, he had a “bad flu” that dragged on and on.
One day after school I was taken straight to mums friends house, I didn’t get home until nearly 12 pm that night and as I had fallen asleep I was put straight into bed in my brother's room, he was asleep too. I had previously voiced my concern that my dad was going to die. It was denied heavily. He died just after 2 am
The flu wasn’t flu, it was end-stage lung cancer so he didn’t get his goodnight kiss the night before (obviously a major factor) and one of his childhood friends told me he was gone for the “BIG sleep”, guess who had major sleeping problems for many years after, because I blamed myself when it was nothing to do with me in reality.
Another very close family member died several years (aforementioned aunt) after my dad, lessons were learned and I was informed what was happening each step of the way, not full details but the “fluffy” version, I was able to help practically and deal very well with this even though I had a very close bond with them,
So OP, like @TheSandgroper "never underestimate the ability of a toddler to confound you, behave well and make you proud" 100% true
I would let her take him OP, death doesn’t occur in convenient slots for funerals, let her take him to the wake too, however, bring something small to help keep him amused.
As the person isn’t someone he knows there isn’t the emotive aspect of it which there would be if someone in the family died and he would have to deal with emotionally charged atmosphere, plus your DM does get a small chance to show him off to her friends circle in that group which can lighten the mood especially at a wake