Is it normal my mum says one thing then says the opposite?

Okay so she has been doing this my whole life, and I'm just going to use one example that happened recently since this would be too long if I listed them all.

Last night I logged into my Facebook just to check if I had any messages, I didn't and was going to log out but my mum was online and messaged me. (My parents are divorced and I live with my dad.)

After chatting to her she asks if me and my sister are coming to sleep over this weekend. I had already visited her last week, and we were suppose to go again next week but my mum wanted us to come over this weekend.

I had already talked to my dad about this and he wants to wait until next week because he's low on fuel and can't afford more, and he wants to take a break going there. (Last week my dad took 4 trips there, it takes 2 hours there and back because my mum lives really far away.)

I told her why my dad didn't want to take us there until next weekend, and she basically began to throw a hissy fit, since my sister didn't come over last week she thinks my dad has brainwashed her into not coming over, (which isn't even true, my sister basically stays in her room all day so it would be impossible lol.) She then starts blaming my dad for more things (when something goes wrong my mum always blames my dad no matter what)

I get pissed and start replying back to her in a sarcastic way until she says she doesn't care if we come over or not, I probably shouldn't of said this but I replied "then stop talking to me and get on with your life." She then told me we don't care about her and we want her to die, remember this is all because me and my sister aren't going to her place this weekend.

Because I was pissed I closed Facebook and after an hour I went back on, my mum had sent me lots of messages like "I'm sorry I just wanted yous to come over because I have lots of food here and to spend time with me, I thought you wanted to see the new kitten", telling me that she was planning on making us our favourite meals, etc. basically trying to make me feel guilty (which it did.)

So is it normal my mum does this shit? She says one thing, then starts throwing a fucking tantrum because she doesn't get her way, blames dad, tells me I'm a horrible person, then apologizes and tries to make me feel like I'm the bad person? She also does this when I'm at her place, I only stay there for like 2 days and honestly I get so tired of her shit I'm glad when I see my dads car pull up to take us home.