I can totally relate to your family's concerns. I do recall feeling it was a bit weird when I saw friends BFing toddlers. However, what I did do is sit and try to work out why I felt like that. I recognised that it was cultural, that I'd not seen it before, and that I was used to breasts being sexual.
So I understand the feeling but I absolutely don't support anyone who doesn't have the maturity to recognise why they feel like they do. It's up to them whether they can move on from it inside their own head (society and culture is hugely strong) but it's absolutely the right thing for them to recognise the logic of term feeding, and support you in it.
I tend to point out that we wouldn't consider not giving a child cow's milk to drink and most people consider it to be an essential part of a child's diet (even though it's not of course). Therefore, it makes most sense to give milk from our own species.
I then might go on to say that not only does our own milk match a child's needs more than milk from a multi-stomached animal, because our milk is designed for a clever, slow-growing animal, not a stupid, fast-growing one, but that breastmilk also has exceptionally helpful immunity support. Given that a child's immune system isn't mature until around age 6, that immunity helps them through all those childhood illnesses, reduces time away from nursery/school and therefore helps you to stay at work (if appropriate).
I might also mention that it's not necessarily frowned on (other than by dentists..!) to give a child a dummy, or bottle, at 2, and that's an artificial nipple.
Oh a whole load of things really, depending on the person and circumstances.
In the end, the person who I would say matters most to get on board is your DH. What pushes his buttons? Would he read science based information on term feeding for instance? What is important to him that could be used to bring him round? He's the one who is best placed to re-direct the MIL comments, but he needs to be with you on it to do so. It can be very lonely, term breastfeeding, so a supportive partner is a big thing.
Another consideration would be to find your local LLL group to see if they hold toddler meetings. I can tell you from personal experience that nothing makes you feel more normal than when you BF your 16 month old "baby" in a room with mothers feeding 3, 4, 5 year olds and older :) When they're looking at your little one and talking about when theirs were babies. Suddenly your nursling seems reeeeally teeny! And it all makes a lot of sense.