My son was unable to have the mist for a few years because he has asthma. But, for the past 3 years he has gotten it and he LOVES it. He is not a fan at all of getting anything sprayed up his nose, but he loves the Mist vs. the flu shot. (He's 8 now).
My daughter got the mist for the 1st time this year (3.5) and she loved it too. I have never really had to do the nasal spray with her, but she was great with the mist. Sniffed when they told her to.
Just so you know, the mist is nothing like the nasal spray you do when they are sick. It doesn't spray nearly has forcefully or hard as the nasal spray does. It really is a very small spray and they sniff slightly and then they are done.
Personally, I think the shot is way worse for them and so I vote for the mist every time. You may want to ask them about the mist for your son in regards to having a 2 month old at home. If you do end up getting the mist, I would just keep your older son out of the face of your younger son for 2-3 days.
Good luck with your decision!