I really empathise with you, I'm having both hips replaced this year (one three months after the other) and my Mum is going to have to move in for 6 months as I will not be physically able to look after DD on my own when DH is at work.
I doubt it as easy as asking the parents to leave - unless you can afford to hire a full time nanny or 5 days a week full time nursery for both baby and toddler, which doesn't even take into account what care needs you yourself have.
I think the bottom line is you NEED to make this work. Have a calm sit down with your mum, re-iterate how grateful you are, and how lucky you are to have parents in a position to, and willing to upend their lives to care for you and your children. But explain that you DH is horribly stressed at the moment by your operation and worry and is very touchy, and while you know she means well he's taking it as critisism so would she mind just avoiding doing it for the next couple of weeks while he's so stressed.
Get your DH as well, explain your Mum is doing you both a massive favour, you literally can't cope without her right now, and he needs to behave like an adult and be courteous to your mum, even if she is being irritating.
The only thing is, if he is genuinely doing something undesirable (you seem to agree with you mum in part regarding his "parenting skills" - is he shouting or doing anything that you consider to be wrong, or is it a difference in parenting styles?) then maybe you ned to tackle that behaviour as a different issue, but, unless it is dangerous behaviour then I would suggest while your in recovery from an operation is not the time to do so, and you need to get your mum to understand that as well.
Could you arrange for your husband to have a few days off work, so that your parents can have a break elsewhere for a few days? Might do everyone some good.