AITA for asking my parents to leave?

I’ll try to make this as brief as possible but basically my parents live 90 mins away and in my final weeks of pregnancy with my 3rd child my mom had the idea to book a hotel in our area around the time I went into labor/delivered my baby. The plan was for them to book a kid-friendly hotel with a pool for 2 nights so they could come pick up our two toddler sons and bring them back with them, giving my husband and I some time to bond with the baby, nest, rest, settle, etc. Great idea, and win-win for everyone, right? My mom and I talked about it multiple times leading up to my labor, she was very excited as she doesn’t get to spend as much time with her grandsons as she would like, given the distance. She kept saying how they were on call, waiting for the news. Baby arrived around 7am Tuesday, they arrived next day around noon to pick up our sons (or so I thought). I expected that likely they would come in, meet my newborn, and be out the door in 30 mins or less, leaving us to rest and recuperate, and spend time with baby. But they came in, took their shoes off, slippers on, drinks poured, lunch popped in the oven. I thought to myself ok…what is happening. I gave the benefit of the doubt telling myself, it is lunch time after all and that’s nice they brought lunch, and maybe they’re leaving after this. But they didn’t. They pretty much moved in and made no mention of taking the boys and when I asked my mom what the plan was, saying the boys’ bags are packed and ready by the front door, she said she couldn’t find a hotel with a pool in the area and so booked a basic one bedroom and didn’t think the boys would care to go there, so thought they’d stick around the house and help with whatever like if I needed her to “hold the baby”. LIKE what does that help with??? We have a small house that I just gave birth in one day prior and hadn’t even showered or washed up, hardly ate, house in complete disarray, I lost a lot of blood and was still recovering and could barely walk (I’m pretty small and had a 10lb baby). My heart sank. I wanted nothing more than to rest up (zero sleep the night of labor), hold my baby in peace, and nurse freely, while my husband planned to clean up the house , change sheets, and start organizing some stuff. But with my two toddlers still around and now my parents visiting, none of that would happen. To make matters worse, my mom brought them cookies and chocolate…my husband and I were livid to put it mildly. So not only did the plan change and we didn’t know until they arrived, they now also have no plan with my children, and now giving them sugar to add even more chaos to the equation. The final straw happened about 2-3 hours after they showed up, my gma called my mom and my mom handed the phone to me, leaving me in the baby’s area I had sectioned off in the living room with my 2 year old who was going through all the baby stuff while I’m attempting to talk to my gma, walk over and stop my son, while my mom is walking into the next room. I’m screaming to myself WHAT ARE WE EVEN DOING RIGHT NOW?? So I politely asked them if they could please take our children somewhere like the park and be gone for a few hours as the house is very chaotic right now. Long story short my mom got very offended saying they came all this way to help us. I said it’s not that I don’t want to see you guys but the plan was to take the boys to a hotel with a pool and she just kept getting defensive saying she couldn’t find one in the area last minute and she tried her best. I said I wish I would have known that before you drove all the way here, because I would’ve told you not to bother, as we weren’t looking for visitors so soon after having a baby, and she was very upset at that as well. Fyi my husband and I checked after they left, and there’s PLENTY of hotels in the area with pools that had availability that day/night. We think she just lied because they were slightly more expensive per night (like $20…) and probably figured it would be fine to impose on us rather than follow through with the original plan, betting on us not saying anything. The thing is, if they didn’t want to do the hotel option, they could’ve altered the plan however to ensure they had a day planned with my kids and not make it our problem. That was the crux of the assignment…and they did not understand the assignment. They then brought them back less than two hours later and I asked that they leave for a little while longer as my midwife was coming for a postpartum check in in an hour and my mom got mad wondering why I didn’t mention that. Honestly I didn’t think I had to considering it was initially irrelevant per the original plan. There’s more but I’ll stop here cuz this is long as heck. So AITA?