Hun, Even writing a will doesn't always guarantee custody to the grandparents hun .
If he is on the birth certificate then he has 50/50 parental rights with you , But if he is not on the scene or involved then this would be taken into consideration, For eg ..he wouldn't just be able to turn up out of the blue & get custody.
Your child would most likely go to your parents first then the court would decide what is in the childs best interests but the fathers involvement prior would be included, If he's not been nowhere near they wouldn't just give child to him, He would start off with access etc then he would have to apply to courts again down the line. Your parents would then have to apply to the court to have parental rights/ guardian rights over your child.
If i'm being perfectly honest whether or not he is being good with you from now until around the time of birth is not enough in my eyes, My sons dad is not on the birth cert for many reasons & now i'm glad it was the best decision ever made! I have 100% rights & say over my son, he was originally involved but in & out of his life, Then he would cause hassle with me & threaten to get custody, & now his dad is nowhere around, hasn't been arsed about him. Bumps dad has already denied baby is his & has completely stopped contact so he wont be on birth cert either, He'll be crawling back to get into bumps life when he's born things will be so diff he wont know whats hit him lol
Do not let your parents force you or push you into anything hun , This has to be entirely your decision. Whether or not they have bought anything
With regards to him seeing baby over xmas then he would have to stay in a b&b if he really wanted to see baby, If he can't afford it then there is nothing else you can do. I personally would not want him staying with me, & i do think your parents are right to refuse him there . So tell him to either find a b&b or is it possible you can go to his for 2 days or something?
Think about the birth certificate thing carefully hun, & remember it your decision nobody elses.