C.B.
wow no offense but does every question have to lead to someone saying you should have your kid evaluated for this or that disorder? it's literally every question on here. i feel like 99% of these issues are just discipline problems.
one thing you don't mention - do you not do time outs? if he has been raised with timeouts (or maybe it's time to start them), part of it is, you STAY where mom puts you. if you can get him to do that then you should be able to keep him from wallowing all over the baby. tell him if he doesn't stay off the baby he will have a time out. separate them (put him in his timeout spot) and keep doing it as long as it takes. do the same thing for pets. there is appropriate "loving" and inappropriate, and he's not being safe. tell him it's not safe to lay on the baby and he could hurt him. i could be wrong, i just feel like you need to be firm and insist he stop this behavior. it's not okay. you will have to stick to your guns and be consistent.
just me, but i would forget about the eye contact for the moment and pick the more important battle of keeping your little one safe. my son is extremely shy and i have a really hard time getting him to look me in the eye, except for the briefest of flutters here and there. focus more on the behavior you can control. you can't force him to look at you. use a calm voice and state matter-of-factly what the results are for his chosen behavior - don't give him reason to be afraid of you or fear judgement. the eye contact will come later.