Cheating ? Trying to possibly fix

I noticed my boyfriend takes his phone with him every where he goes..

if he goes to take trash out he grabs his phone, if he goes to the bathroom even if he just has to pee he takes his phone.. if he’s sleeping, his phone is either under him or next to him..

his phone is on silent 24/7 unless i say something and he’ll put the ringer on but a couple hours later I’ll notice it’s back on silent and I’m just at a point where i don’t say anything anymore.

one day he snatched his phone from me when all i was doing was texting his friend back for him and i just feel like he’s cheating but with him constantly taking his phone with him everywhere he goes i can’t really prove it and when i bring it up it’s I’m not cheating and etc.. he’ll go out and be gone for hours coming back 2 or 5 in the morning and say he was with his friend but don’t tell me where he was and doesn’t text me while he’s out..

one time he was telling me a story and he told on himself.. he said he was at the studio that day recording for other people but turns out he was with more people and they tried to go to this 5 star restaurant and they went on a boat ride… and how they was drinking and all that other stuff while i was home all day watching our 2 kids which are 1 years old and 4 months.

If i want to go out it’s always why you want to go out ? Or if I’m trying to find girl-friends and go out with them he has a problem.. even if i have the kids with me he’ll continuously text me and if i don’t respond in a reasonable time it’s a issue and he says I’m cheating and everything is tiring… i even told him if he wants to break up I’m cool with that and he said no he doesn’t want to and he wants to work everything out but idk how if he’s constantly hiding or lying about something.