AITA For Expecting My Mother to Pay For Our Pram

I (34F) & my husband (36M) are expecting our first baby in June. This is my mother’s first grandchild. We don’t have the best relationship, when I was born having a baby didn’t suit her lifestyle, so I was raised by my nan, her mother. I did interact with her throughout my childhood, but as she was an alcoholic, most of my interactions were visiting her at rehab. My nan passed when I was 21, and I flew down for her funeral, she had always asked me to be kind to my mother so I felt a sense of obligation to at least be amicable with her. So from then until now I have tried to do that. FF I’m pregnant, she’s excited. I’m still wary of her but I’m trying, my husband thinks she’s changed and encourages me to be more understanding. One day she asks to take me to one of my doctors appointments, I agree as my husband is working. The day of, he’s able to attend, but I don’t cancel, as I knew she’d be disappointed, she heard the heartbeat and she spent the whole time telling stories of when she was pregnant with me. FF to the xmas, we’re thinking about putting pieces on layby, Cot, Carseat, Pram. My husband and I aren’t "well off" but we manage our finances, we buy off marketplace where we can but for the the pieces we want to last, we’re prepared to buy new. My mother was over for coffee and asked us if we had looked at these things, we said we were starting to, she said as her gift to us she’d like to get us the pram. We were both surprised and very grateful, reminding her she didn’t have to and that we’re ok to get it but she insisted. She asked us to go and try some and let her know which one. So we did, We landed on one which isn’t cheap, about $1,700.00 We told her we had picked this one, but as it was expensive had no expectations for her to pay and we were okay to cover it. She declined, we insisted we could at least go halves, she declined. All she asked was that we put it on layby so she could pay it off. We were grateful and we agreed. We waited to put it on layby, incase over boxing day it went on sale, it didnt. However she still insisted we go that day. Boxing day comes, she arrives at our house 45mins early (as I’m getting up) I ask her why she’s so early, she says "fine, nevermind" and leaves! I text her and apologise if I was rude, as I was just surprised. She doesn’t respond. On my birthday, a few days later, she gives me a gc to put the pram on layby $500 and tells me to let her know when that’s done and she’ll make payments. We do this and let her know. 1mth passes into the 3mth layby and she’s not made any payments, we let her know we put the carseat on layby as well and are making payments and ask if she needs the details for the pram. She says "as agreed, I’ll pay for half so I’ll give you a gc for $400 and you can put it on the layby" I never expected her to pay for the pram in the first place, and we offered to pay half and now all of a sudden she’s changed her mind and is acting like this was the agreement all along