I'd recommend trusting your husband on this, not your MIL, friends, or MN.
Your DH shut down his mother, and says that he support you. Yeah, he's also said it's not ideal and it'll be nice...but they're only young once.
From what's been written, I don't think he could be more clear that he accepts this as the best option for now and more than happy to support you in it. You can ask him further about it if you want to be more certain. but only if you're willing to trust the answer over others.
You may need to find more of a work around if you want to bring the sex life back; however, exhaustion from having a toddler and a baby is just as much of a moodkiller.
I do agree with the PP that if it's going to change now or when it changes later, there will need to be a talk about what that looks like. However it's going to work, there will need to adaptations, whether that how the load will be split, doing things like having a mattress or one of those foam folding chairs that folds out into one next the toddler's bed to doze on while getting used to this change, it will have some bumps. Few at that age are plop into bed and no more issues all night.
Tell me you haven't had a two year old without telling me... Two year olds know how to have tantrums to get what they want.
Only if the tantrums have worked before that. Tantrums aren't active manipulation at first, tiny children aren't that sophisticated to come up with the idea that tantrums will get what they want. At first, tantrums are more emotional dysregulation because they don't understand why the adult doesn't want what they want/doesn't automatically know what they want and they don't know how to handle the emotions and the physical sensations of those emotions - anger and frustration can be pretty uncomfortable. Tantrums can become manipulation, but only if they learn that they'll work to manage that discomfort, and they learn that through living the pattern of adults giving in to them repeatedly.
Oh, and I have four children, I've had my toddler years.