i take it the OP is not a single person.
she has a partner.
that is the difference.
she has to think very carefully. or else the relationship with her partner may not survive.
i thought on first reading that it wa a typo, and that the child was 3 years not months.
the parents need to learn how to look after their own child properly.
if they hand him over to you, you may be left holding the baby alone, without a partner.
and then if they move, or change their mind, take the baby back, and you are left bereft.
i guess your partner did not envisage becoming an add-on step GF, with care of a child in his living quarters. he could reasonably have supposed that stage was in the past.
it's tricky all round.