IPhone 4 not receiving messages? - 1

Ok so I recently bought two phones, the iPhone 4, off of ebay. I kept one and gave the other to my mom. We were using non-smart phones before, so I had to cut both our sim cards down to make them fit in the iphone. Everything seems to work fine with both of them, except for the fact that they don't always receive text messages. So basically, here's the situation: when our phones are in Wi-Fi and have iMessage on, we receive everyone's texts. When our iPhones are outside of Wi-Fi (hence imessage won't work outside of Wi-Fi) we don't get everyone's texts, particularly people who are using other iphones. I haven't been able to confirm that its only them whose messages I don't get but I'm fairly certain it is. What's weird is that my mom and I can receive each other's texts when were outside of Wi-Fi, but only if we're physically right next to each other, and even then it seems to take too long for the messages to get to one another. But as soon as one of us doesn't have Wi-Fi, the person without the Wi-Fi can't receive messages, only send them. I've tried everything, turning iMessage on and off, turning cellular data on and off, etc. I even tried restoring her phone but to no avail. When we first got our phones, her phone asked her if she wanted to link iMessage from her iphone to imessage from her ipad. I though that might have been the problem but when I restored her iphone, it still suffered the same issue.

Added (1). I also have an iPod touch, but my phone never asked to link iMessage with it. Only happened to my mom with her ipad/iphone.

I phones don't work

Whatever happens don't get an iPhone 6