on end for MAY early on JUNE is suitable travel to Taiwan with family, small kid and older parents?

It may not be good choice to travel there as your plan, for there will be dense rainfall. If you don't mind, change your plan to end of Apr. to early May, when the rain is relatively light. Although the rainy days would still be frequent, they won't last for a whole day. More importantly, it would be the best timing to see the cherry blossom.