Is my husband cheating on me?

So I have been married for three years and my husband and I have always had a laid back 'solid' relationship.
After years of struggle to get pregnant we finally fell pregnant with our little miracle baby.
Throughout my pregnancy my husband was an utter bastard, refusing to buy anything for our child stressing me out, constantly talking about his ex wife!
Long story short our precious little girl is here now and my husband has so very little to do with her and hates to buy her anything won't leave me any money to buy essentials for our child, the house myself but yet he openly pays his ex wife maintenance for a child he never wanted doesn't love and doesn't see. He finishes work and doesn't communicate with us he just sits on his phone all night that goes everywhere with him and acts like a child so I have to look after him aswell. He seems to always be active on messenger but when I asked to see what he was doing surprise surprise there was no messages. He doesn't notice if I make an effort for him anymore, he doesn't say nice things.
I am seriously contemplating packing his bags and changing the locks. I try to speak to him but instead I get ignored or snapped at.
What is this mans issue now?
Is my husband cheating on me?
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